diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 87f47dc65cea9..a6eaa8f2f57f8 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -125,6 +125,7 @@ Other enhancements
 - Attempting to write into a file in missing parent directory with :meth:`DataFrame.to_csv`, :meth:`DataFrame.to_html`, :meth:`DataFrame.to_excel`, :meth:`DataFrame.to_feather`, :meth:`DataFrame.to_parquet`, :meth:`DataFrame.to_stata`, :meth:`DataFrame.to_json`, :meth:`DataFrame.to_pickle`, and :meth:`DataFrame.to_xml` now explicitly mentions missing parent directory, the same is true for :class:`Series` counterparts (:issue:`24306`)
 - :meth:`IntegerArray.all` , :meth:`IntegerArray.any`, :meth:`FloatingArray.any`, and :meth:`FloatingArray.all` use Kleene logic (:issue:`41967`)
 - Added support for nullable boolean and integer types in :meth:`DataFrame.to_stata`, :class:`~pandas.io.stata.StataWriter`, :class:`~pandas.io.stata.StataWriter117`, and :class:`~pandas.io.stata.StataWriterUTF8` (:issue:`40855`)
+- :meth:`DataFrame.to_parquet` now writes Parquet compliant data for columns which contain lists or arrays when using PyArrow 4.0.0 or greater (:issue:`43689`)
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/compat/__init__.py b/pandas/compat/__init__.py
index 3233de8e3b6d1..c1fee9ad4121e 100644
--- a/pandas/compat/__init__.py
+++ b/pandas/compat/__init__.py
@@ -24,6 +24,7 @@
     pa_version_under2p0,
     pa_version_under3p0,
     pa_version_under4p0,
+    pa_version_under5p0,
 )
 
 PY39 = sys.version_info >= (3, 9)
@@ -155,4 +156,5 @@ def get_lzma_file(lzma):
     "pa_version_under2p0",
     "pa_version_under3p0",
     "pa_version_under4p0",
+    "pa_version_under5p0",
 ]
diff --git a/pandas/io/parquet.py b/pandas/io/parquet.py
index e92afd4e35ca1..0dfb6b6678074 100644
--- a/pandas/io/parquet.py
+++ b/pandas/io/parquet.py
@@ -13,6 +13,7 @@
     FilePathOrBuffer,
     StorageOptions,
 )
+from pandas.compat import pa_version_under4p0
 from pandas.compat._optional import import_optional_dependency
 from pandas.errors import AbstractMethodError
 from pandas.util._decorators import doc
@@ -179,6 +180,12 @@ def write(
             mode="wb",
             is_dir=partition_cols is not None,
         )
+
+        # Output compliant Parquet if PyArrow supports it and the user hasn't
+        # explicitly set the desired behavior
+        if not pa_version_under4p0 and "use_compliant_nested_type" not in kwargs:
+            kwargs["use_compliant_nested_type"] = True
+
         try:
             if partition_cols is not None:
                 # writes to multiple files under the given path
diff --git a/pandas/tests/io/test_parquet.py b/pandas/tests/io/test_parquet.py
index 01715ee133e96..f263ca66b00a0 100644
--- a/pandas/tests/io/test_parquet.py
+++ b/pandas/tests/io/test_parquet.py
@@ -931,6 +931,18 @@ def test_read_parquet_manager(self, pa, using_array_manager):
         else:
             assert isinstance(result._mgr, pd.core.internals.BlockManager)
 
+    @td.skip_if_no("pyarrow", min_version="4.0.0")
+    def test_list_column_results_in_compliant_parquet(self, pa):
+        # https://github.com/pandas-dev/pandas/issues/43689
+        df = pd.DataFrame({"a": [[1], [2]]})
+
+        with tm.ensure_clean() as path:
+            df.to_parquet(path, pa)
+            result = pyarrow.parquet.read_table(path)
+
+        assert str(result.schema.field_by_name("a").type) == "list<element: int64>"
+        check_round_trip(df, pa)
+
 
 class TestParquetFastParquet(Base):
     def test_basic(self, fp, df_full):