diff --git a/jax/_src/api.py b/jax/_src/api.py
index c59ae055c695..51f1ae81ebf2 100644
--- a/jax/_src/api.py
+++ b/jax/_src/api.py
@@ -2531,8 +2531,30 @@ def fun(*tangents):
 
   return apply_flat_fun(fun, io_tree, *py_args)
 
-def _vjp_pullback_wrapper(cotangent_dtypes, cotangent_shapes,
-                          io_tree, fun, py_args):
+def _vjp_pullback_wrapper(name, cotangent_dtypes, cotangent_shapes, io_tree,
+                          fun, *py_args_):
+  if len(py_args_) != 1:
+    msg = (f"The function returned by `jax.vjp` applied to {name} was called "
+           f"with {len(py_args_)} arguments, but functions returned by "
+           "`jax.vjp` must be called with a single argument corresponding to "
+           f"the single value returned by {name} (even if that returned "
+           "value is a tuple or other container).\n"
+           "\n"
+           "For example, if we have:\n"
+           "\n"
+           "  def f(x):\n"
+           "    return (x, x)\n"
+           "  _, f_vjp = jax.vjp(f, 1.0)\n"
+           "\n"
+           "the function `f` returns a single tuple as output, and so we call "
+           "`f_vjp` with a single tuple as its argument:\n"
+           "\n"
+           "  x_bar, = f_vjp((2.0, 2.0))\n"
+           "\n"
+           "If we instead call `f_vjp(2.0, 2.0)`, with the values 'splatted "
+           "out' as arguments rather than in a tuple, this error can arise.")
+    raise TypeError(msg)
+  py_args, = py_args_
   in_tree_expected, out_tree = io_tree
   args, in_tree = tree_flatten(py_args)
   if in_tree != in_tree_expected:
@@ -2637,9 +2659,8 @@ def _vjp(fun: lu.WrappedFun, *primals, has_aux=False, reduce_axes=()):
   ct_shapes = [np.shape(x) for x in out_primal]
   # Ensure that vjp_py is a PyTree so that we can pass it from the forward to the
   # backward pass in a custom VJP.
-  vjp_py = Partial(partial(_vjp_pullback_wrapper,
-                           ct_dtypes, ct_shapes,
-                           (out_tree, in_tree)),
+  vjp_py = Partial(partial(_vjp_pullback_wrapper, fun.__name__,
+                           ct_dtypes, ct_shapes, (out_tree, in_tree)),
                    out_vjp)
   if not has_aux:
     return out_primal_py, vjp_py
diff --git a/tests/api_test.py b/tests/api_test.py
index 3fc7ad6a0973..1dc048d83a44 100644
--- a/tests/api_test.py
+++ b/tests/api_test.py
@@ -4095,6 +4095,14 @@ def h(x):
 
     b(8)  # don't crash
 
+  def test_vjp_multiple_arguments_error_message(self):
+    # https://github.com/google/jax/issues/13099
+    def foo(x):
+      return (x, x)
+    _, f_vjp = jax.vjp(foo, 1.0)
+    with self.assertRaisesRegex(TypeError, "applied to foo"):
+      f_vjp(1.0, 1.0)
+
 
 @jtu.with_config(jax_experimental_subjaxpr_lowering_cache=True)
 class SubcallTraceCacheTest(jtu.JaxTestCase):