diff --git a/cpp/src/arrow/array/array_test.cc b/cpp/src/arrow/array/array_test.cc
index 2cdf94bfab95..98cc7d8254f9 100644
--- a/cpp/src/arrow/array/array_test.cc
+++ b/cpp/src/arrow/array/array_test.cc
@@ -2558,6 +2558,32 @@ TEST(TestPrimitiveAdHoc, FloatingUlpDistanceEquality) {
   CheckFloatApproxEqualsWithUlpDistance<DoubleType>();
 }
 
+TEST(TestRunEncodedBuilder, MergeConsecutiveNaNs) {
+  auto run_end_encoded_type = run_end_encoded(int32(), float32());
+  std::shared_ptr<RunEndEncodedArray> result;
+  auto run_end_builder = std::make_shared<Int32Builder>();
+  auto value_builder = std::make_shared<FloatBuilder>();
+  RunEndEncodedBuilder builder(default_memory_pool(), run_end_builder, value_builder,
+                               run_end_encoded_type);
+  ASSERT_OK(builder.AppendScalar(**MakeScalar(float32(), 1), 15));
+  ASSERT_OK(builder.AppendScalar(**MakeScalar(float32(), 1), 10));
+  ASSERT_OK(builder.AppendScalar(**MakeScalar(float32(), 2), 20));
+  ASSERT_OK(builder.AppendScalar(**MakeScalar(float32(), std::nanf("")), 25));
+  ASSERT_OK(builder.AppendScalar(**MakeScalar(float32(), std::nanf("")), 5));
+  ASSERT_OK(builder.AppendScalar(**MakeScalar(float32(), 3), 15));
+  ASSERT_OK(builder.AppendScalar(**MakeScalar(float32(), std::nanf("")), 20));
+  ASSERT_OK(builder.AppendScalar(**MakeScalar(float32(), 4), 25));
+  ASSERT_OK(builder.Finish(&result));
+
+  std::shared_ptr<Array> expected_run_end_array;
+  std::shared_ptr<Array> expected_value_array;
+  ArrayFromVector<Int32Type>({25, 45, 75, 90, 110, 135}, &expected_run_end_array);
+  ArrayFromVector<FloatType>({1.0, 2.0, std::nanf(""), 3.0, std::nanf(""), 4.0},
+                             &expected_value_array);
+  AssertArraysEqual(*expected_run_end_array, *result->run_ends());
+  AssertArraysEqual(*expected_value_array, *result->values());
+}
+
 // ----------------------------------------------------------------------
 // FixedSizeBinary tests
 
diff --git a/cpp/src/arrow/array/builder_run_end.cc b/cpp/src/arrow/array/builder_run_end.cc
index 2edeaff504d2..8b38783eb898 100644
--- a/cpp/src/arrow/array/builder_run_end.cc
+++ b/cpp/src/arrow/array/builder_run_end.cc
@@ -23,6 +23,8 @@
 #include <utility>
 #include <vector>
 
+#include "arrow/array/array_run_end.h"
+#include "arrow/array/util.h"
 #include "arrow/scalar.h"
 #include "arrow/util/checked_cast.h"
 #include "arrow/util/int_util_overflow.h"
@@ -102,7 +104,7 @@ Status RunCompressorBuilder::AppendScalar(const Scalar& scalar, int64_t n_repeat
     current_value_ = scalar.is_valid ? scalar.shared_from_this() : NULLPTR;
     current_run_length_ = n_repeats;
   } else if ((current_value_ == NULLPTR && !scalar.is_valid) ||
-             (current_value_ != NULLPTR && current_value_->Equals(scalar))) {
+             (current_value_ != NULLPTR && current_value_->Equals(scalar, options_))) {
     // Extend the currently open run
     current_run_length_ += n_repeats;
   } else {
diff --git a/cpp/src/arrow/array/builder_run_end.h b/cpp/src/arrow/array/builder_run_end.h
index ac92efbd0dbe..43e59df1c6ef 100644
--- a/cpp/src/arrow/array/builder_run_end.h
+++ b/cpp/src/arrow/array/builder_run_end.h
@@ -23,8 +23,10 @@
 #include <utility>
 #include <vector>
 
-#include "arrow/array.h"
+#include "arrow/array/array_base.h"
+#include "arrow/array/array_run_end.h"
 #include "arrow/array/builder_base.h"
+#include "arrow/compare.h"
 
 namespace arrow {
 
@@ -161,6 +163,7 @@ class RunCompressorBuilder : public ArrayBuilder {
   std::shared_ptr<ArrayBuilder> inner_builder_;
   std::shared_ptr<const Scalar> current_value_ = NULLPTR;
   int64_t current_run_length_ = 0;
+  const EqualOptions options_ = EqualOptions::Defaults().nans_equal(true);
 };
 
 }  // namespace internal