diff --git a/cpp/src/arrow/util/value_parsing.h b/cpp/src/arrow/util/value_parsing.h
index 195cdc843ac..1b300074851 100644
--- a/cpp/src/arrow/util/value_parsing.h
+++ b/cpp/src/arrow/util/value_parsing.h
@@ -815,6 +815,9 @@ static inline bool ParseTimestampStrptime(const char* buf, size_t length,
   std::string clean_copy(buf, length);
   struct tm result;
   memset(&result, 0, sizeof(struct tm));
+  // Default the day to the first for formats without a day directive, so that
+  // an explicitly parsed zero day is not mistaken for an omitted one
+  result.tm_mday = 1;
 #ifdef _WIN32
   char* ret = arrow_strptime(clean_copy.c_str(), format, &result);
 #else
@@ -826,10 +829,17 @@ static inline bool ParseTimestampStrptime(const char* buf, size_t length,
   if (!allow_trailing_chars && static_cast<size_t>(ret - clean_copy.c_str()) != length) {
     return false;
   }
+  // Reject impossible dates such as February 30 or a zero day, which strptime
+  // may accept (the day of month is checked against 31 at most), instead of
+  // rolling them over into the next month; consistent with the ISO-8601 parser.
+  const arrow_vendored::date::year_month_day ymd =
+      arrow_vendored::date::year(result.tm_year + 1900) / (result.tm_mon + 1) /
+      result.tm_mday;
+  if (!ymd.ok()) {
+    return false;
+  }
   // ignore the time part
-  arrow_vendored::date::sys_seconds secs =
-      arrow_vendored::date::sys_days(arrow_vendored::date::year(result.tm_year + 1900) /
-                                     (result.tm_mon + 1) / std::max(result.tm_mday, 1));
+  arrow_vendored::date::sys_seconds secs = arrow_vendored::date::sys_days(ymd);
   if (!ignore_time_in_day) {
     secs += (std::chrono::hours(result.tm_hour) + std::chrono::minutes(result.tm_min) +
              std::chrono::seconds(result.tm_sec));
diff --git a/cpp/src/arrow/util/value_parsing_test.cc b/cpp/src/arrow/util/value_parsing_test.cc
index 6eb387fc031..69baba169ff 100644
--- a/cpp/src/arrow/util/value_parsing_test.cc
+++ b/cpp/src/arrow/util/value_parsing_test.cc
@@ -856,7 +856,8 @@ TEST(TimestampParser, StrptimeParser) {
   };
 
   std::vector<Case> cases = {{"5/31/2000 12:34:56", "2000-05-31 12:34:56"},
-                             {"5/31/2000 00:00:00", "2000-05-31 00:00:00"}};
+                             {"5/31/2000 00:00:00", "2000-05-31 00:00:00"},
+                             {"2/29/2000 12:34:56", "2000-02-29 12:34:56"}};
 
   for (auto unit : TimeUnit::values()) {
     for (const auto& case_ : cases) {
@@ -869,7 +870,17 @@ TEST(TimestampParser, StrptimeParser) {
   }
 
   // Unparseable strings
-  std::vector<std::string> unparseables = {"foo", "5/1/2000", "5/1/2000 12:34:56:6"};
+  std::vector<std::string> unparseables = {"foo", "5/1/2000", "5/1/2000 12:34:56:6",
+                                           // Impossible dates are rejected rather
+                                           // than rolled over into the next month
+                                           "2/30/2000 12:34:56", "4/31/2000 12:34:56",
+                                           "2/29/2001 12:34:56",
+                                           // A zero day is rejected rather than
+                                           // taken as the first of the month
+                                           "2/00/2000 12:34:56",
+                                           // A zero month is rejected rather than
+                                           // taken as December of the previous year
+                                           "0/15/2000 12:34:56"};
   for (auto& value : unparseables) {
     int64_t dummy;
     ASSERT_FALSE((*parser)(value.c_str(), value.size(), TimeUnit::SECOND, &dummy));
@@ -908,6 +919,15 @@ TEST(TimestampParser, StrptimeLocaleDirectives) {
   }
 }
 
+TEST(TimestampParser, StrptimeWithoutDay) {
+  // A format without a day directive gives the first of the month
+  auto parser = TimestampParser::MakeStrptime("%Y-%m");
+  int64_t converted, expected;
+  ASSERT_TRUE((*parser)("2000-02", 7, TimeUnit::SECOND, &converted));
+  ASSERT_TRUE(ParseTimestampISO8601("2000-02-01", 10, TimeUnit::SECOND, &expected));
+  ASSERT_EQ(expected, converted);
+}
+
 TEST(TimestampParser, StrptimeZoneOffset) {
   if (!kStrptimeSupportsZone) {
     GTEST_SKIP() << "strptime does not support %z on this platform";
diff --git a/cpp/src/arrow/vendored/musl/strptime.c b/cpp/src/arrow/vendored/musl/strptime.c
index eb325108b8a..f592f79600d 100644
--- a/cpp/src/arrow/vendored/musl/strptime.c
+++ b/cpp/src/arrow/vendored/musl/strptime.c
@@ -212,7 +212,7 @@ char *strptime(const char *__restrict s, const char *__restrict f, struct tm *__
 			*dest = 0;
 			for (i=1; i<=min+range && isdigit(*s); i*=10)
 				*dest = *dest * 10 + *s++ - '0';
-			if (*dest - min >= range) return 0;
+			if ((unsigned)(*dest - min) >= (unsigned)range) return 0;
 			*dest -= adj;
 			switch((char *)dest - (char *)tm) {
 			case offsetof(struct tm, tm_yday):