diff --git a/doc/source/whatsnew/v1.3.3.rst b/doc/source/whatsnew/v1.3.3.rst
index 00409cf963ab3..46080e1847317 100644
--- a/doc/source/whatsnew/v1.3.3.rst
+++ b/doc/source/whatsnew/v1.3.3.rst
@@ -17,6 +17,7 @@ Fixed regressions
 - Fixed regression in :class:`DataFrame` constructor failing to broadcast for defined :class:`Index` and len one list of :class:`Timestamp` (:issue:`42810`)
 - Performance regression in :meth:`core.window.ewm.ExponentialMovingWindow.mean` (:issue:`42333`)
 - Fixed regression in :meth:`.GroupBy.agg` incorrectly raising in some cases (:issue:`42390`)
+- Fixed regression in :meth:`.GroupBy.quantile` which was failing with ``pandas.NA`` (:issue:`42849`)
 - Fixed regression in :meth:`merge` where ``on`` columns with ``ExtensionDtype`` or ``bool`` data types were cast to ``object`` in ``right`` and ``outer`` merge (:issue:`40073`)
 - Fixed regression in :meth:`RangeIndex.where` and :meth:`RangeIndex.putmask` raising ``AssertionError`` when result did not represent a :class:`RangeIndex` (:issue:`43240`)
 - Fixed regression in :meth:`read_parquet` where the ``fastparquet`` engine would not work properly with fastparquet 0.7.0 (:issue:`43075`)
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index 42de5137ba670..79ee71ddb1047 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -63,6 +63,7 @@ class providing the base-class of operations.
 from pandas.core.dtypes.common import (
     is_bool_dtype,
     is_datetime64_dtype,
+    is_float_dtype,
     is_integer_dtype,
     is_numeric_dtype,
     is_object_dtype,
@@ -2453,6 +2454,9 @@ def pre_processor(vals: ArrayLike) -> tuple[np.ndarray, np.dtype | None]:
             elif is_timedelta64_dtype(vals.dtype):
                 inference = np.dtype("timedelta64[ns]")
                 out = np.asarray(vals).astype(float)
+            elif isinstance(vals, ExtensionArray) and is_float_dtype(vals):
+                inference = np.dtype(np.float64)
+                out = vals.to_numpy(dtype=float, na_value=np.nan)
             else:
                 out = np.asarray(vals)
 
diff --git a/pandas/tests/groupby/test_quantile.py b/pandas/tests/groupby/test_quantile.py
index 90437b9139594..83d6c20bcac24 100644
--- a/pandas/tests/groupby/test_quantile.py
+++ b/pandas/tests/groupby/test_quantile.py
@@ -248,6 +248,45 @@ def test_groupby_quantile_skips_invalid_dtype(q):
     tm.assert_frame_equal(result, expected)
 
 
+def test_groupby_quantile_NA_float(any_float_dtype):
+    # GH#42849
+    df = DataFrame({"x": [1, 1], "y": [0.2, np.nan]}, dtype=any_float_dtype)
+    result = df.groupby("x")["y"].quantile(0.5)
+    expected = pd.Series([0.2], dtype=float, index=[1.0], name="y")
+    expected.index.name = "x"
+    tm.assert_series_equal(expected, result)
+
+    result = df.groupby("x")["y"].quantile([0.5, 0.75])
+    expected = pd.Series(
+        [0.2] * 2,
+        index=pd.MultiIndex.from_product(([1.0], [0.5, 0.75]), names=["x", None]),
+        name="y",
+    )
+    tm.assert_series_equal(result, expected)
+
+
+def test_groupby_quantile_NA_int(any_int_ea_dtype):
+    # GH#42849
+    df = DataFrame({"x": [1, 1], "y": [2, 5]}, dtype=any_int_ea_dtype)
+    result = df.groupby("x")["y"].quantile(0.5)
+    expected = pd.Series([3.5], dtype=float, index=Index([1], name="x"), name="y")
+    tm.assert_series_equal(expected, result)
+
+    result = df.groupby("x").quantile(0.5)
+    expected = DataFrame({"y": 3.5}, index=Index([1], name="x"))
+    tm.assert_frame_equal(result, expected)
+
+
+@pytest.mark.parametrize("dtype", ["Float64", "Float32"])
+def test_groupby_quantile_allNA_column(dtype):
+    # GH#42849
+    df = DataFrame({"x": [1, 1], "y": [pd.NA] * 2}, dtype=dtype)
+    result = df.groupby("x")["y"].quantile(0.5)
+    expected = pd.Series([np.nan], dtype=float, index=[1.0], name="y")
+    expected.index.name = "x"
+    tm.assert_series_equal(expected, result)
+
+
 def test_groupby_timedelta_quantile():
     # GH: 29485
     df = DataFrame(