diff --git a/cpp/src/arrow/array/array_list_test.cc b/cpp/src/arrow/array/array_list_test.cc
index 930702e7cb8d2..def01379e0634 100644
--- a/cpp/src/arrow/array/array_list_test.cc
+++ b/cpp/src/arrow/array/array_list_test.cc
@@ -716,6 +716,30 @@ TEST_F(TestMapArray, BuildingStringToInt) {
   ASSERT_ARRAYS_EQUAL(*actual, expected);
 }
 
+TEST_F(TestMapArray, BuildingWithFieldNames) {
+  // Builder should preserve field names in output Array
+  ASSERT_OK_AND_ASSIGN(auto map_type,
+                       MapType::Make(field("some_entries",
+                                           struct_({field("some_key", int16(), false),
+                                                    field("some_value", int16())}),
+                                           false)));
+
+  auto key_builder = std::make_shared<Int16Builder>();
+  auto item_builder = std::make_shared<Int16Builder>();
+  MapBuilder map_builder(default_memory_pool(), key_builder, item_builder, map_type);
+
+  std::shared_ptr<Array> actual;
+  ASSERT_OK(map_builder.Append());
+  ASSERT_OK(key_builder->AppendValues({0, 1, 2, 3, 4, 5}));
+  ASSERT_OK(item_builder->AppendValues({1, 1, 2, 3, 5, 8}));
+  ASSERT_OK(map_builder.AppendNull());
+  ASSERT_OK(map_builder.Finish(&actual));
+  ASSERT_OK(actual->ValidateFull());
+
+  ASSERT_EQ(actual->type()->ToString(), map_type->ToString());
+  ASSERT_EQ(map_builder.type()->ToString(), map_type->ToString());
+}
+
 TEST_F(TestMapArray, ValidateErrorNullStruct) {
   ASSERT_OK_AND_ASSIGN(
       auto values,
diff --git a/cpp/src/arrow/array/builder_nested.cc b/cpp/src/arrow/array/builder_nested.cc
index a3bcde0381a4a..fbba1fd056430 100644
--- a/cpp/src/arrow/array/builder_nested.cc
+++ b/cpp/src/arrow/array/builder_nested.cc
@@ -38,6 +38,10 @@ MapBuilder::MapBuilder(MemoryPool* pool, const std::shared_ptr<ArrayBuilder>& ke
                        const std::shared_ptr<DataType>& type)
     : ArrayBuilder(pool), key_builder_(key_builder), item_builder_(item_builder) {
   auto map_type = internal::checked_cast<const MapType*>(type.get());
+  entries_name_ = map_type->field(0)->name();
+  key_name_ = map_type->key_field()->name();
+  item_name_ = map_type->item_field()->name();
+  item_nullable_ = map_type->item_field()->nullable();
   keys_sorted_ = map_type->keys_sorted();
 
   std::vector<std::shared_ptr<ArrayBuilder>> child_builders{key_builder, item_builder};
@@ -59,6 +63,10 @@ MapBuilder::MapBuilder(MemoryPool* pool,
                        const std::shared_ptr<DataType>& type)
     : ArrayBuilder(pool) {
   auto map_type = internal::checked_cast<const MapType*>(type.get());
+  entries_name_ = map_type->field(0)->name();
+  key_name_ = map_type->key_field()->name();
+  item_name_ = map_type->item_field()->name();
+  item_nullable_ = map_type->item_field()->nullable();
   keys_sorted_ = map_type->keys_sorted();
   key_builder_ = struct_builder->child_builder(0);
   item_builder_ = struct_builder->child_builder(1);
diff --git a/cpp/src/arrow/array/builder_nested.h b/cpp/src/arrow/array/builder_nested.h
index 9e3a4458d8da1..78efc0e2cbb9a 100644
--- a/cpp/src/arrow/array/builder_nested.h
+++ b/cpp/src/arrow/array/builder_nested.h
@@ -330,7 +330,14 @@ class ARROW_EXPORT MapBuilder : public ArrayBuilder {
   ArrayBuilder* value_builder() const { return list_builder_->value_builder(); }
 
   std::shared_ptr<DataType> type() const override {
-    return map(key_builder_->type(), item_builder_->type(), keys_sorted_);
+    // Key and Item builder may update types, but they don't contain the field names,
+    // so we need to reconstruct the type. (See ARROW-13735.)
+    return std::make_shared<MapType>(
+        field(entries_name_,
+              struct_({field(key_name_, key_builder_->type(), false),
+                       field(item_name_, item_builder_->type(), item_nullable_)}),
+              false),
+        keys_sorted_);
   }
 
   Status ValidateOverflow(int64_t new_elements) {
@@ -342,6 +349,10 @@ class ARROW_EXPORT MapBuilder : public ArrayBuilder {
 
  protected:
   bool keys_sorted_ = false;
+  bool item_nullable_ = false;
+  std::string entries_name_;
+  std::string key_name_;
+  std::string item_name_;
   std::shared_ptr<ListBuilder> list_builder_;
   std::shared_ptr<ArrayBuilder> key_builder_;
   std::shared_ptr<ArrayBuilder> item_builder_;
diff --git a/python/pyarrow/tests/test_array.py b/python/pyarrow/tests/test_array.py
index 6b87a0ba9b0e3..aeeb6314c83d1 100644
--- a/python/pyarrow/tests/test_array.py
+++ b/python/pyarrow/tests/test_array.py
@@ -907,6 +907,15 @@ def test_list_from_arrays(list_array_type, list_type_factory):
         result.validate(full=True)
 
 
+def test_map_labelled():
+    #  ARROW-13735
+    t = pa.map_(pa.field("name", "string", nullable=False), "int64")
+    arr = pa.array([[('a', 1), ('b', 2)], [('c', 3)]], type=t)
+    assert arr.type.key_field == pa.field("name", pa.utf8(), nullable=False)
+    assert arr.type.item_field == pa.field("value", pa.int64())
+    assert len(arr) == 2
+
+
 def test_map_from_arrays():
     offsets_arr = np.array([0, 2, 5, 8], dtype='i4')
     offsets = pa.array(offsets_arr, type='int32')