diff --git a/icu4c/source/common/cmemory.h b/icu4c/source/common/cmemory.h
index bc1c91c1500..ac36d10f7ab 100644
--- a/icu4c/source/common/cmemory.h
+++ b/icu4c/source/common/cmemory.h
@@ -50,6 +50,7 @@
 #define UPRV_LENGTHOF(array) (int32_t)(sizeof(array)/sizeof((array)[0]))
 #define uprv_memset(buffer, mark, size) U_STANDARD_CPP_NAMESPACE memset(buffer, mark, size)
 #define uprv_memcmp(buffer1, buffer2, size) U_STANDARD_CPP_NAMESPACE memcmp(buffer1, buffer2,size)
+#define uprv_memchr(ptr, value, num) U_STANDARD_CPP_NAMESPACE memchr(ptr, value, num)
 
 U_CAPI void * U_EXPORT2
 uprv_malloc(size_t s) U_MALLOC_ATTR U_ALLOC_SIZE_ATTR(1);
diff --git a/icu4c/source/i18n/currunit.cpp b/icu4c/source/i18n/currunit.cpp
index 7f3490d406b..a5b039fcab2 100644
--- a/icu4c/source/i18n/currunit.cpp
+++ b/icu4c/source/i18n/currunit.cpp
@@ -18,8 +18,10 @@
 #include "unicode/ustring.h"
 #include "cstring.h"
 #include "uinvchar.h"
+#include "charstr.h"
 
 static constexpr char16_t kDefaultCurrency[] = u"XXX";
+static constexpr char kDefaultCurrency8[] = "XXX";
 
 U_NAMESPACE_BEGIN
 
@@ -50,6 +52,30 @@ CurrencyUnit::CurrencyUnit(ConstChar16Ptr _isoCode, UErrorCode& ec) {
     initCurrency(simpleIsoCode);
 }
 
+CurrencyUnit::CurrencyUnit(StringPiece _isoCode, UErrorCode& ec) {
+    // Note: unlike the old constructor, reject empty arguments with an error.
+    char isoCodeBuffer[4];
+    const char* isoCodeToUse;
+    // uprv_memchr checks that the string contains no internal NULs
+    if (_isoCode.length() != 3 || uprv_memchr(_isoCode.data(), 0, 3) != nullptr) {
+        isoCodeToUse = kDefaultCurrency8;
+        ec = U_ILLEGAL_ARGUMENT_ERROR;
+    } else if (!uprv_isInvariantString(_isoCode.data(), 3)) {
+        // TODO: Perform a more strict ASCII check like in ICU4J isAlpha3Code?
+        isoCodeToUse = kDefaultCurrency8;
+        ec = U_INVARIANT_CONVERSION_ERROR;
+    } else {
+        // Have to use isoCodeBuffer to ensure the string is NUL-terminated
+        uprv_strncpy(isoCodeBuffer, _isoCode.data(), 3);
+        isoCodeBuffer[3] = 0;
+        isoCodeToUse = isoCodeBuffer;
+    }
+    // TODO: Perform uppercasing here like in ICU4J Currency.getInstance()?
+    u_charsToUChars(isoCodeToUse, isoCode, 3);
+    isoCode[3] = 0;
+    initCurrency(isoCodeToUse);
+}
+
 CurrencyUnit::CurrencyUnit(const CurrencyUnit& other) : MeasureUnit(other) {
     u_strcpy(isoCode, other.isoCode);
 }
diff --git a/icu4c/source/i18n/number_formatimpl.cpp b/icu4c/source/i18n/number_formatimpl.cpp
index c64703699cd..de6ec65486b 100644
--- a/icu4c/source/i18n/number_formatimpl.cpp
+++ b/icu4c/source/i18n/number_formatimpl.cpp
@@ -178,7 +178,7 @@ NumberFormatterImpl::macrosToMicroGenerator(const MacroProps& macros, bool safe,
     bool isAccounting =
             macros.sign == UNUM_SIGN_ACCOUNTING || macros.sign == UNUM_SIGN_ACCOUNTING_ALWAYS ||
             macros.sign == UNUM_SIGN_ACCOUNTING_EXCEPT_ZERO;
-    CurrencyUnit currency(nullptr, status);
+    CurrencyUnit currency(u"", status);
     if (isCurrency) {
         currency = CurrencyUnit(macros.unit, status); // Restore CurrencyUnit from MeasureUnit
     }
diff --git a/icu4c/source/i18n/unicode/currunit.h b/icu4c/source/i18n/unicode/currunit.h
index ac3bfedd7b3..bf6bd9ac323 100644
--- a/icu4c/source/i18n/unicode/currunit.h
+++ b/icu4c/source/i18n/unicode/currunit.h
@@ -44,6 +44,7 @@ class U_I18N_API CurrencyUnit: public MeasureUnit {
 
     /**
      * Construct an object with the given ISO currency code.
+     *
      * @param isoCode the 3-letter ISO 4217 currency code; must have
      * length 3 and need not be NUL-terminated. If NULL, the currency
      * is initialized to the unknown currency XXX.
@@ -53,6 +54,17 @@ class U_I18N_API CurrencyUnit: public MeasureUnit {
      */
     CurrencyUnit(ConstChar16Ptr isoCode, UErrorCode &ec);
 
+    /**
+     * Construct an object with the given ISO currency code.
+     *
+     * @param isoCode the 3-letter ISO 4217 currency code; must have
+     * length 3. If invalid, the currency is initialized to XXX.
+     * @param ec input-output error code. If the isoCode is invalid,
+     * then this will be set to a failing value.
+     * @draft ICU 64
+     */
+    CurrencyUnit(StringPiece isoCode, UErrorCode &ec);
+
     /**
      * Copy constructor
      * @stable ICU 3.0
diff --git a/icu4c/source/test/depstest/dependencies.txt b/icu4c/source/test/depstest/dependencies.txt
index 7bdcf66a509..a54f024f1ff 100644
--- a/icu4c/source/test/depstest/dependencies.txt
+++ b/icu4c/source/test/depstest/dependencies.txt
@@ -57,7 +57,7 @@ group: c_strings
     __ctype_b_loc  # for <ctype.h>
     # We must not use tolower and toupper because they are system-locale-sensitive (Turkish i).
     strlen strchr strrchr strstr strcmp strncmp strcpy strncpy strcat strncat
-    memcmp memcpy memmove memset
+    memchr memcmp memcpy memmove memset
     # Additional symbols in an optimized build.
     __strcpy_chk __strncpy_chk __strcat_chk __strncat_chk
     __rawmemchr __memcpy_chk __memmove_chk __memset_chk
diff --git a/icu4c/source/test/intltest/numfmtst.cpp b/icu4c/source/test/intltest/numfmtst.cpp
index 3cb3ea9af17..c3533039923 100644
--- a/icu4c/source/test/intltest/numfmtst.cpp
+++ b/icu4c/source/test/intltest/numfmtst.cpp
@@ -2119,12 +2119,63 @@ void NumberFormatTest::TestCurrencyUnit(void){
     static const UChar BAD2[] = u"??A";
     static const UChar XXX[]  = u"XXX";
     static const char XXX8[]  =  "XXX";
+    static const UChar INV[]  = u"{$%";
+    static const char INV8[]  =  "{$%";
+    static const UChar ZZZ[]  = u"zz";
+    static const char ZZZ8[]  = "zz";
+
+    UChar* EUR = (UChar*) malloc(6);
+    EUR[0] = u'E';
+    EUR[1] = u'U';
+    EUR[2] = u'R';
+    char* EUR8 = (char*) malloc(3);
+    EUR8[0] = 'E';
+    EUR8[1] = 'U';
+    EUR8[2] = 'R';
+
     CurrencyUnit cu(USD, ec);
     assertSuccess("CurrencyUnit", ec);
 
     assertEquals("getISOCurrency()", USD, cu.getISOCurrency());
     assertEquals("getSubtype()", USD8, cu.getSubtype());
 
+    CurrencyUnit inv(INV, ec);
+    assertEquals("non-invariant", U_INVARIANT_CONVERSION_ERROR, ec);
+    assertEquals("non-invariant", XXX, inv.getISOCurrency());
+    ec = U_ZERO_ERROR;
+
+    CurrencyUnit zzz(ZZZ, ec);
+    assertEquals("too short", U_ILLEGAL_ARGUMENT_ERROR, ec);
+    assertEquals("too short", XXX, zzz.getISOCurrency());
+    ec = U_ZERO_ERROR;
+
+    CurrencyUnit eur(EUR, ec);
+    assertEquals("non-nul-terminated", u"EUR", eur.getISOCurrency());
+    assertEquals("non-nul-terminated", "EUR", eur.getSubtype());
+
+    // Test StringPiece constructor
+    CurrencyUnit cu8(USD8, ec);
+    assertEquals("StringPiece constructor", USD, cu8.getISOCurrency());
+
+    CurrencyUnit inv8(INV8, ec);
+    assertEquals("non-invariant 8", U_INVARIANT_CONVERSION_ERROR, ec);
+    assertEquals("non-invariant 8", XXX, inv8.getISOCurrency());
+    ec = U_ZERO_ERROR;
+
+    CurrencyUnit zzz8(ZZZ8, ec);
+    assertEquals("too short 8", U_ILLEGAL_ARGUMENT_ERROR, ec);
+    assertEquals("too short 8", XXX, zzz8.getISOCurrency());
+    ec = U_ZERO_ERROR;
+
+    CurrencyUnit zzz8b({ZZZ8, 3}, ec);
+    assertEquals("too short 8b", U_ILLEGAL_ARGUMENT_ERROR, ec);
+    assertEquals("too short 8b", XXX, zzz8b.getISOCurrency());
+    ec = U_ZERO_ERROR;
+
+    CurrencyUnit eur8({EUR8, 3}, ec);
+    assertEquals("non-nul-terminated 8", u"EUR", eur8.getISOCurrency());
+    assertEquals("non-nul-terminated 8", "EUR", eur8.getSubtype());
+
     CurrencyUnit cu2(cu);
     if (!(cu2 == cu)){
         errln("CurrencyUnit copy constructed object should be same");
@@ -2177,6 +2228,9 @@ void NumberFormatTest::TestCurrencyUnit(void){
     CurrencyUnit failure(*meter, ec);
     assertEquals("Copying from meter should fail", ec, U_ILLEGAL_ARGUMENT_ERROR);
     assertEquals("Copying should not give uninitialized ISO code", u"", failure.getISOCurrency());
+
+    uprv_free(EUR);
+    uprv_free(EUR8);
 }
 
 void NumberFormatTest::TestCurrencyAmount(void){