diff --git a/python/pyspark/pandas/series.py b/python/pyspark/pandas/series.py
index 4828b59d5ad26..0f2c8e02b18a8 100644
--- a/python/pyspark/pandas/series.py
+++ b/python/pyspark/pandas/series.py
@@ -3396,11 +3396,18 @@ def autocorr(self, lag: int = 1) -> float:
         else:
             lag_scol = F.lag(scol, lag).over(Window.orderBy(NATURAL_ORDER_COLUMN_NAME))
             lag_col_name = verify_temp_column_name(sdf, "__autocorr_lag_tmp_col__")
-            corr = (
-                sdf.withColumn(lag_col_name, lag_scol)
-                .select(F.corr(scol, F.col(lag_col_name)))
-                .head()[0]
-            )
+
+            sdf_lag = sdf.withColumn(lag_col_name, lag_scol)
+            if is_ansi_mode_enabled(sdf.sparkSession):
+                # Compute covariance between the original and lagged columns.
+                # If the covariance is None or zero (indicating no linear relationship),
+                # return NaN, otherwise, proceeding to compute correlation may raise
+                # DIVIDE_BY_ZERO under ANSI mode.
+                cov_value = sdf_lag.select(F.covar_samp(scol, F.col(lag_col_name))).head()[0]
+                if cov_value is None or cov_value == 0.0:
+                    return np.nan
+            corr = sdf_lag.select(F.corr(scol, F.col(lag_col_name))).head()[0]
+
         return np.nan if corr is None else corr
 
     def corr(
diff --git a/python/pyspark/pandas/tests/series/test_stat.py b/python/pyspark/pandas/tests/series/test_stat.py
index cc03e64b48869..7c92edbeea3a4 100644
--- a/python/pyspark/pandas/tests/series/test_stat.py
+++ b/python/pyspark/pandas/tests/series/test_stat.py
@@ -607,6 +607,9 @@ def test_autocorr(self):
         with self.assertRaisesRegex(TypeError, r"lag should be an int; however, got"):
             psser.autocorr(1.0)
 
+        psser = ps.Series([1, 0, 0, 0])
+        self.assertTrue(bool(np.isnan(psser.autocorr())))
+
     def _test_autocorr(self, pdf):
         psdf = ps.from_pandas(pdf)
         for lag in range(-10, 10):