diff --git a/cpp/src/arrow/util/value_parsing.h b/cpp/src/arrow/util/value_parsing.h
index 1c2102fe370..d845a71cf1f 100644
--- a/cpp/src/arrow/util/value_parsing.h
+++ b/cpp/src/arrow/util/value_parsing.h
@@ -848,6 +848,12 @@ static inline bool ParseTimestampStrptime(const char* buf, size_t length,
   // ignore the time part
   arrow_vendored::date::sys_seconds secs = arrow_vendored::date::sys_days(ymd);
   if (!ignore_time_in_day) {
+    // Reject leap seconds, which Arrow cannot represent, instead of adding them
+    // to the time of day (which wraps them into the next minute); consistent
+    // with the ISO-8601 parser.
+    if (result.tm_sec >= 60) {
+      return false;
+    }
     secs += (std::chrono::hours(result.tm_hour) + std::chrono::minutes(result.tm_min) +
              std::chrono::seconds(result.tm_sec));
 #if !defined(_WIN32) && !defined(_AIX)
diff --git a/cpp/src/arrow/util/value_parsing_test.cc b/cpp/src/arrow/util/value_parsing_test.cc
index 875418f3195..2a2d39777bf 100644
--- a/cpp/src/arrow/util/value_parsing_test.cc
+++ b/cpp/src/arrow/util/value_parsing_test.cc
@@ -870,17 +870,20 @@ TEST(TimestampParser, StrptimeParser) {
   }
 
   // Unparseable strings
-  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"};
+  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",
+      // Leap seconds are rejected, as by the
+      // ISO-8601 parser
+      "5/31/2000 12:30:60", "5/31/2000 23:59:60", "5/31/2000 23:59:61"};
   for (auto& value : unparseables) {
     int64_t dummy;
     ASSERT_FALSE((*parser)(value.c_str(), value.size(), TimeUnit::SECOND, &dummy));
diff --git a/cpp/src/gandiva/to_date_holder_test.cc b/cpp/src/gandiva/to_date_holder_test.cc
index 1612d9b4f44..ada3e55d2fd 100644
--- a/cpp/src/gandiva/to_date_holder_test.cc
+++ b/cpp/src/gandiva/to_date_holder_test.cc
@@ -85,6 +85,15 @@ TEST_F(TestToDateHolder, TestSimpleDateTime) {
   millis_since_epoch =
       to_date(&execution_context_, s.data(), (int)s.length(), true, &out_valid);
   EXPECT_EQ(millis_since_epoch, 534643200000);
+
+  // A leap second does not make the value invalid, as the time is ignored
+  EXPECT_OK_AND_ASSIGN(auto to_date_holder24,
+                       ToDateHolder::Make("YYYY-MM-DD HH24:MI:SS", 1));
+  s = std::string("2020-12-31 23:59:60");
+  millis_since_epoch = (*to_date_holder24)(&execution_context_, s.data(), (int)s.length(),
+                                           true, &out_valid);
+  EXPECT_TRUE(out_valid);
+  EXPECT_EQ(millis_since_epoch, 1609372800000);
 }
 
 TEST_F(TestToDateHolder, TestSimpleDate) {