diff --git a/cpp/src/arrow/compute/kernels/scalar_string_test.cc b/cpp/src/arrow/compute/kernels/scalar_string_test.cc
index a98b5937327..4581e6377a7 100644
--- a/cpp/src/arrow/compute/kernels/scalar_string_test.cc
+++ b/cpp/src/arrow/compute/kernels/scalar_string_test.cc
@@ -1895,11 +1895,17 @@ TYPED_TEST(TestStringKernels, StrptimeZoneOffset) {
   // N.B. BSD strptime only supports (+/-)HHMM and not the wider range
   // of values GNU strptime supports.
   std::string input1 = R"(["5/1/2020 +0100", null, "12/11/1900 -0130"])";
-  std::string output1 =
+  std::string output =
       R"(["2020-04-30T23:00:00.000000", null, "1900-12-11T01:30:00.000000"])";
-  StrptimeOptions options("%m/%d/%Y %z", TimeUnit::MICRO, /*error_is_null=*/true);
-  this->CheckUnary("strptime", input1, timestamp(TimeUnit::MICRO, "UTC"), output1,
-                   &options);
+  StrptimeOptions options1("%m/%d/%Y %z", TimeUnit::MICRO, /*error_is_null=*/true);
+  this->CheckUnary("strptime", input1, timestamp(TimeUnit::MICRO, "UTC"), output,
+                   &options1);
+
+  // format without whitespace before %z (GH-35448)
+  std::string input2 = R"(["2020-05-01T00:00+0100", null, "1900-12-11T00:00-0130"])";
+  StrptimeOptions options2("%Y-%m-%dT%H:%M%z", TimeUnit::MICRO, /*error_is_null=*/true);
+  this->CheckUnary("strptime", input2, timestamp(TimeUnit::MICRO, "UTC"), output,
+                   &options2);
 }
 
 TYPED_TEST(TestStringKernels, StrptimeDoesNotProvideDefaultOptions) {
diff --git a/cpp/src/arrow/compute/kernels/scalar_temporal_unary.cc b/cpp/src/arrow/compute/kernels/scalar_temporal_unary.cc
index 3addaf68630..a88ce389360 100644
--- a/cpp/src/arrow/compute/kernels/scalar_temporal_unary.cc
+++ b/cpp/src/arrow/compute/kernels/scalar_temporal_unary.cc
@@ -1237,7 +1237,6 @@ const std::string GetZone(const std::string& format) {
         zone = "UTC";
         break;
       }
-      cur++;
     } else {
       count = 0;
     }