diff --git a/doc/source/whatsnew/v1.1.4.rst b/doc/source/whatsnew/v1.1.4.rst
index c0aa1afc34c8f..458d735b42b7f 100644
--- a/doc/source/whatsnew/v1.1.4.rst
+++ b/doc/source/whatsnew/v1.1.4.rst
@@ -19,6 +19,7 @@ Fixed regressions
 - Fixed regression where :meth:`DataFrame.agg` would fail with :exc:`TypeError` when passed positional arguments to be passed on to the aggregation function (:issue:`36948`).
 - Fixed regression in :class:`RollingGroupby` with ``sort=False`` not being respected (:issue:`36889`)
 - Fixed regression in :meth:`Series.astype` converting ``None`` to ``"nan"`` when casting to string (:issue:`36904`)
+- Fixed regression in :meth:`Series.rank` method failing for read-only data (:issue:`37290`)
 - Fixed regression in :class:`RollingGroupby` causing a segmentation fault with Index of dtype object (:issue:`36727`)
 - Fixed regression in :meth:`DataFrame.resample(...).apply(...)` raised ``AttributeError`` when input was a :class:`DataFrame` and only a :class:`Series` was evaluated (:issue:`36951`)
 - Fixed regression in :class:`PeriodDtype` comparing both equal and unequal to its string representation (:issue:`37265`)
diff --git a/pandas/_libs/algos.pyx b/pandas/_libs/algos.pyx
index da5ae97bb067b..f0cf485d9584a 100644
--- a/pandas/_libs/algos.pyx
+++ b/pandas/_libs/algos.pyx
@@ -325,7 +325,7 @@ def nancorr(const float64_t[:, :] mat, bint cov=False, minp=None):
 
 @cython.boundscheck(False)
 @cython.wraparound(False)
-def nancorr_spearman(const float64_t[:, :] mat, Py_ssize_t minp=1) -> ndarray:
+def nancorr_spearman(ndarray[float64_t, ndim=2] mat, Py_ssize_t minp=1) -> ndarray:
     cdef:
         Py_ssize_t i, j, xi, yi, N, K
         ndarray[float64_t, ndim=2] result
@@ -799,7 +799,7 @@ ctypedef fused rank_t:
 @cython.wraparound(False)
 @cython.boundscheck(False)
 def rank_1d(
-    rank_t[:] in_arr,
+    ndarray[rank_t, ndim=1] in_arr,
     ties_method="average",
     bint ascending=True,
     na_option="keep",
@@ -1018,7 +1018,7 @@ def rank_1d(
 
 
 def rank_2d(
-    rank_t[:, :] in_arr,
+    ndarray[rank_t, ndim=2] in_arr,
     int axis=0,
     ties_method="average",
     bint ascending=True,
diff --git a/pandas/tests/test_algos.py b/pandas/tests/test_algos.py
index caaca38d07fa5..aefbcee76b5d7 100644
--- a/pandas/tests/test_algos.py
+++ b/pandas/tests/test_algos.py
@@ -1691,11 +1691,13 @@ def _check(arr):
         _check(np.array([np.nan, np.nan, 5.0, 5.0, 5.0, np.nan, 1, 2, 3, np.nan]))
         _check(np.array([4.0, np.nan, 5.0, 5.0, 5.0, np.nan, 1, 2, 4.0, np.nan]))
 
-    def test_basic(self):
+    def test_basic(self, writable):
         exp = np.array([1, 2], dtype=np.float64)
 
         for dtype in np.typecodes["AllInteger"]:
-            s = Series([1, 100], dtype=dtype)
+            data = np.array([1, 100], dtype=dtype)
+            data.setflags(write=writable)
+            s = Series(data)
             tm.assert_numpy_array_equal(algos.rank(s), exp)
 
     def test_uint64_overflow(self):