diff --git a/jax/_src/nn/initializers.py b/jax/_src/nn/initializers.py
index 25ce3632b0aa..25ecb4013d1f 100644
--- a/jax/_src/nn/initializers.py
+++ b/jax/_src/nn/initializers.py
@@ -222,9 +222,12 @@ def _compute_fans(shape: Sequence[int],
   Axes not in in_axis, out_axis, or batch_axis are assumed to constitute the
   "receptive field" of a convolution (kernel spatial dimensions).
   """
-  if len(shape) <= 1:
-    raise ValueError(f"Can't compute input and output sizes of a {len(shape)}"
-                     "-dimensional weights tensor. Must be at least 2D.")
+  if in_axis == -2 and len(shape) <= 1:
+    raise ValueError(
+        f"Can't compute input and output sizes of a {len(shape)}-dimensional"
+        " weights tensor with default in_axis. Must be at least 2D or specify"
+        " in_axis explicitly."
+    )
 
   if isinstance(in_axis, int):
     in_size = shape[in_axis]
diff --git a/tests/nn_test.py b/tests/nn_test.py
index 1c4261451cc0..7671721665b4 100644
--- a/tests/nn_test.py
+++ b/tests/nn_test.py
@@ -781,7 +781,7 @@ def testLog1mExpGrad(self):
   "InitializerRecord",
   ["name", "initializer", "shapes", "dtypes"])
 
-ALL_SHAPES = [(2,), (2, 2), (2, 3), (3, 2), (2, 3, 4), (4, 3, 2), (2, 3, 4, 5)]
+ALL_SHAPES = [(), (2,), (2, 2), (2, 3), (3, 2), (2, 3, 4), (4, 3, 2), (2, 3, 4, 5)]
 
 def initializer_record(name, initializer, dtypes, min_dims=2, max_dims=4):
   shapes = [shape for shape in ALL_SHAPES
@@ -805,6 +805,24 @@ def initializer_record(name, initializer, dtypes, min_dims=2, max_dims=4):
         partial(nn.initializers.variance_scaling, 1, "fan_geo_avg", "normal"),
         jtu.dtypes.floating,
     ),
+    initializer_record(
+        "variance_scaling_fan_in",
+        partial(nn.initializers.variance_scaling, 1, "fan_in", "normal", in_axis=[0], out_axis=[]),
+        jtu.dtypes.floating,
+        min_dims=1,
+    ),
+    initializer_record(
+        "variance_scaling_fan_in",
+        partial(nn.initializers.variance_scaling, 1, "fan_in", "normal", in_axis=[], out_axis=[0]),
+        jtu.dtypes.floating,
+        min_dims=1,
+    ),
+    initializer_record(
+        "variance_scaling_fan_in",
+        partial(nn.initializers.variance_scaling, 1, "fan_in", "normal", in_axis=[], out_axis=[]),
+        jtu.dtypes.floating,
+        min_dims=0,
+    ),
 ]
 
 
@@ -869,8 +887,9 @@ def testVarianceScalingError(self):
 
     with self.assertRaisesRegex(
       ValueError,
-      "Can't compute input and output sizes of a 1"
-      "-dimensional weights tensor. Must be at least 2D."
+      "Can't compute input and output sizes of a 1-dimensional"
+      " weights tensor with default in_axis. Must be at least 2D or specify"
+      " in_axis explicitly.",
     ):
       initializer(rng, shape)