diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 9b1819a7d4d9f..451cd544ef650 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -424,7 +424,7 @@ ExtensionArray
 
 - Bug in :meth:`DataFrame.where` when ``other`` is a :class:`Series` with :class:`ExtensionArray` dtype (:issue:`38729`)
 - Fixed bug where :meth:`Series.idxmax`, :meth:`Series.idxmin` and ``argmax/min`` fail when the underlying data is :class:`ExtensionArray` (:issue:`32749`, :issue:`33719`, :issue:`36566`)
--
+- Bug in cumulative functions (``cumsum``, ``cumprod``, ``cummax`` and ``cummin``)  with extension dtypes not handling ``NA`` correctly and returning object dtype (:issue:`39479`)
 
 Other
 ^^^^^
diff --git a/pandas/core/nanops.py b/pandas/core/nanops.py
index 8d3363df0d132..adb1fc3dc7edd 100644
--- a/pandas/core/nanops.py
+++ b/pandas/core/nanops.py
@@ -18,6 +18,7 @@
     is_bool_dtype,
     is_complex,
     is_datetime64_any_dtype,
+    is_extension_array_dtype,
     is_float,
     is_float_dtype,
     is_integer,
@@ -32,7 +33,7 @@
 from pandas.core.dtypes.dtypes import PeriodDtype
 from pandas.core.dtypes.missing import isna, na_value_for_dtype, notna
 
-from pandas.core.construction import extract_array
+from pandas.core.construction import extract_array, sanitize_array
 
 bn = import_optional_dependency("bottleneck", errors="warn")
 _BOTTLENECK_INSTALLED = bn is not None
@@ -1728,6 +1729,21 @@ def na_accum_func(values: ArrayLike, accum_func, *, skipna: bool) -> ArrayLike:
                 result, dtype=orig_dtype
             )
 
+    elif is_extension_array_dtype(values.dtype):
+        if is_integer_dtype(values.dtype) and np.isinf(mask_a):
+            mask_a = {
+                np.maximum.accumulate: np.iinfo(values.dtype.type).min,
+                np.minimum.accumulate: np.iinfo(values.dtype.type).max,
+            }[accum_func]
+
+        vals = values.copy()
+        mask = isna(vals)
+        mask_copy = np.copy(mask)
+        vals[mask] = mask_a
+        result = accum_func(vals, axis=0)
+        result[mask_copy] = mask_b
+        result = sanitize_array(result, None, values.dtype)
+
     elif skipna and not issubclass(values.dtype.type, (np.integer, np.bool_)):
         vals = values.copy()
         mask = isna(vals)
diff --git a/pandas/tests/frame/test_cumulative.py b/pandas/tests/frame/test_cumulative.py
index 248f3500c41df..32dda8eae2eb4 100644
--- a/pandas/tests/frame/test_cumulative.py
+++ b/pandas/tests/frame/test_cumulative.py
@@ -7,8 +7,9 @@
 """
 
 import numpy as np
+import pytest
 
-from pandas import DataFrame, Series
+from pandas import NA, DataFrame, Series
 import pandas._testing as tm
 
 
@@ -133,3 +134,20 @@ def test_cumulative_ops_preserve_dtypes(self):
             }
         )
         tm.assert_frame_equal(result, expected)
+
+    @pytest.mark.parametrize(
+        "func, exp",
+        [
+            ("cumsum", [2, NA, 7, 6, 6]),
+            ("cumprod", [2, NA, 10, -10, 0]),
+            ("cummin", [2, NA, 2, -1, -1]),
+            ("cummax", [2, NA, 5, 5, 5]),
+        ],
+    )
+    @pytest.mark.parametrize("dtype", ["Float64", "Int64"])
+    def test_cummulative_ops_extension_dtype(self, frame_or_series, dtype, func, exp):
+        # GH#39479
+        obj = frame_or_series([2, np.nan, 5, -1, 0], dtype=dtype)
+        result = getattr(obj, func)()
+        expected = frame_or_series(exp, dtype=dtype)
+        tm.assert_equal(result, expected)