diff --git a/doc/source/whatsnew/v1.0.2.rst b/doc/source/whatsnew/v1.0.2.rst
index 1b6098e6b6ac1..808e6ae709ce9 100644
--- a/doc/source/whatsnew/v1.0.2.rst
+++ b/doc/source/whatsnew/v1.0.2.rst
@@ -74,6 +74,7 @@ Bug fixes
 **I/O**
 
 - Using ``pd.NA`` with :meth:`DataFrame.to_json` now correctly outputs a null value instead of an empty object (:issue:`31615`)
+- Fixed pickling of ``pandas.NA``. Previously a new object was returned, which broke computations relying on ``NA`` being a singleton (:issue:`31847`)
 - Fixed bug in parquet roundtrip with nullable unsigned integer dtypes (:issue:`31896`).
 
 **Experimental dtypes**
diff --git a/pandas/_libs/missing.pyx b/pandas/_libs/missing.pyx
index 4d17a6f883c1c..c54cb652d7b21 100644
--- a/pandas/_libs/missing.pyx
+++ b/pandas/_libs/missing.pyx
@@ -364,6 +364,9 @@ class NAType(C_NAType):
         exponent = 31 if is_32bit else 61
         return 2 ** exponent - 1
 
+    def __reduce__(self):
+        return "NA"
+
     # Binary arithmetic and comparison ops -> propagate
 
     __add__ = _create_binary_propagating_op("__add__")
diff --git a/pandas/tests/scalar/test_na_scalar.py b/pandas/tests/scalar/test_na_scalar.py
index dcb9d66708724..07656de2e9062 100644
--- a/pandas/tests/scalar/test_na_scalar.py
+++ b/pandas/tests/scalar/test_na_scalar.py
@@ -1,3 +1,5 @@
+import pickle
+
 import numpy as np
 import pytest
 
@@ -267,3 +269,26 @@ def test_integer_hash_collision_set():
     assert len(result) == 2
     assert NA in result
     assert hash(NA) in result
+
+
+def test_pickle_roundtrip():
+    # https://github.com/pandas-dev/pandas/issues/31847
+    result = pickle.loads(pickle.dumps(pd.NA))
+    assert result is pd.NA
+
+
+def test_pickle_roundtrip_pandas():
+    result = tm.round_trip_pickle(pd.NA)
+    assert result is pd.NA
+
+
+@pytest.mark.parametrize(
+    "values, dtype", [([1, 2, pd.NA], "Int64"), (["A", "B", pd.NA], "string")]
+)
+@pytest.mark.parametrize("as_frame", [True, False])
+def test_pickle_roundtrip_containers(as_frame, values, dtype):
+    s = pd.Series(pd.array(values, dtype=dtype))
+    if as_frame:
+        s = s.to_frame(name="A")
+    result = tm.round_trip_pickle(s)
+    tm.assert_equal(result, s)