diff --git a/doc/release/upcoming_changes/27661.compatibility.rst b/doc/release/upcoming_changes/27661.compatibility.rst
new file mode 100644
index 000000000000..0482f876766c
--- /dev/null
+++ b/doc/release/upcoming_changes/27661.compatibility.rst
@@ -0,0 +1,5 @@
+* `numpy.cov` now properly transposes single-row (2d array) design matrices
+  when ``rowvar=False``. Previously, single-row design matrices would
+  return a scalar in this scenario, which is not correct, so this
+  is a behavior change and an array of the appropriate shape will
+  now be returned.
diff --git a/numpy/lib/_function_base_impl.py b/numpy/lib/_function_base_impl.py
index ce9b3c0cd8c9..aedd8663ecc5 100644
--- a/numpy/lib/_function_base_impl.py
+++ b/numpy/lib/_function_base_impl.py
@@ -2736,7 +2736,7 @@ def cov(m, y=None, rowvar=True, bias=False, ddof=None, fweights=None,
             dtype = np.result_type(m, y, np.float64)
 
     X = array(m, ndmin=2, dtype=dtype)
-    if not rowvar and X.shape[0] != 1:
+    if not rowvar and m.ndim != 1:
         X = X.T
     if X.shape[0] == 0:
         return np.array([]).reshape(0, 0)
diff --git a/numpy/lib/tests/test_function_base.py b/numpy/lib/tests/test_function_base.py
index 172992ff5fd0..9c33321df77f 100644
--- a/numpy/lib/tests/test_function_base.py
+++ b/numpy/lib/tests/test_function_base.py
@@ -2509,6 +2509,12 @@ def test_cov_dtype(self, test_type):
         res = cov(cast_x1, dtype=test_type)
         assert test_type == res.dtype
 
+    def test_gh_27658(self):
+        x = np.ones((3, 1))
+        expected = np.cov(x, ddof=0, rowvar=True)
+        actual = np.cov(x.T, ddof=0, rowvar=False)
+        assert_allclose(actual, expected, strict=True)
+
 
 class Test_I0: