diff --git a/doc/whats_new/v1.4.rst b/doc/whats_new/v1.4.rst
index adb362d2802d5..953c4906d3fb2 100644
--- a/doc/whats_new/v1.4.rst
+++ b/doc/whats_new/v1.4.rst
@@ -320,6 +320,13 @@ Changelog
   with `np.int64` indices are not supported.
   :pr:`27240` by :user:`Yao Xiao <Charlie-XIAO>`.
 
+:mod:`sklearn.covariance`
+.........................
+
+- |Enhancement| Allow :func:`covariance.shrunk_covariance` to process
+  multiple covariance matrices at once by handling nd-arrays.
+  :pr:`25275` by :user:`Quentin Barthélemy <qbarthelemy>`.
+
 - |API| |FIX| :class:`~compose.ColumnTransformer` now replaces `"passthrough"`
   with a corresponding :class:`~preprocessing.FunctionTransformer` in the
   fitted ``transformers_`` attribute.
diff --git a/sklearn/covariance/_shrunk_covariance.py b/sklearn/covariance/_shrunk_covariance.py
index 5a568192dd3c3..3a79afa30729f 100644
--- a/sklearn/covariance/_shrunk_covariance.py
+++ b/sklearn/covariance/_shrunk_covariance.py
@@ -109,14 +109,14 @@ def _oas(X, *, assume_centered=False):
     prefer_skip_nested_validation=True,
 )
 def shrunk_covariance(emp_cov, shrinkage=0.1):
-    """Calculate a covariance matrix shrunk on the diagonal.
+    """Calculate covariance matrices shrunk on the diagonal.
 
     Read more in the :ref:`User Guide <shrunk_covariance>`.
 
     Parameters
     ----------
-    emp_cov : array-like of shape (n_features, n_features)
-        Covariance matrix to be shrunk.
+    emp_cov : array-like of shape (..., n_features, n_features)
+        Covariance matrices to be shrunk, at least 2D ndarray.
 
     shrinkage : float, default=0.1
         Coefficient in the convex combination used for the computation
@@ -124,8 +124,8 @@ def shrunk_covariance(emp_cov, shrinkage=0.1):
 
     Returns
     -------
-    shrunk_cov : ndarray of shape (n_features, n_features)
-        Shrunk covariance.
+    shrunk_cov : ndarray of shape (..., n_features, n_features)
+        Shrunk covariance matrices.
 
     Notes
     -----
@@ -135,12 +135,13 @@ def shrunk_covariance(emp_cov, shrinkage=0.1):
 
     where `mu = trace(cov) / n_features`.
     """
-    emp_cov = check_array(emp_cov)
-    n_features = emp_cov.shape[0]
+    emp_cov = check_array(emp_cov, allow_nd=True)
+    n_features = emp_cov.shape[-1]
 
-    mu = np.trace(emp_cov) / n_features
     shrunk_cov = (1.0 - shrinkage) * emp_cov
-    shrunk_cov.flat[:: n_features + 1] += shrinkage * mu
+    mu = np.trace(emp_cov, axis1=-2, axis2=-1) / n_features
+    mu = np.expand_dims(mu, axis=tuple(range(mu.ndim, emp_cov.ndim)))
+    shrunk_cov += shrinkage * mu * np.eye(n_features)
 
     return shrunk_cov
 
diff --git a/sklearn/covariance/tests/test_covariance.py b/sklearn/covariance/tests/test_covariance.py
index 0866c209a10c3..ef4bd63149d60 100644
--- a/sklearn/covariance/tests/test_covariance.py
+++ b/sklearn/covariance/tests/test_covariance.py
@@ -81,7 +81,25 @@ def test_covariance():
     assert_array_equal(cov.location_, np.zeros(X.shape[1]))
 
 
+@pytest.mark.parametrize("n_matrices", [1, 3])
+def test_shrunk_covariance_func(n_matrices):
+    """Check `shrunk_covariance` function."""
+
+    n_features = 2
+    cov = np.ones((n_features, n_features))
+    cov_target = np.array([[1, 0.5], [0.5, 1]])
+
+    if n_matrices > 1:
+        cov = np.repeat(cov[np.newaxis, ...], n_matrices, axis=0)
+        cov_target = np.repeat(cov_target[np.newaxis, ...], n_matrices, axis=0)
+
+    cov_shrunk = shrunk_covariance(cov, 0.5)
+    assert_allclose(cov_shrunk, cov_target)
+
+
 def test_shrunk_covariance():
+    """Check consistency between `ShrunkCovariance` and `shrunk_covariance`."""
+
     # Tests ShrunkCovariance module on a simple dataset.
     # compare shrunk covariance obtained from data and from MLE estimate
     cov = ShrunkCovariance(shrinkage=0.5)