diff --git a/tests/BUILD b/tests/BUILD
index 8e60580d40bc..55eaf75fee84 100644
--- a/tests/BUILD
+++ b/tests/BUILD
@@ -48,6 +48,15 @@ jax_test(
     srcs = ["api_util_test.py"],
 )
 
+py_test(
+    name = "array_api_test",
+    srcs = ["array_api_test.py"],
+    deps = [
+        "//jax",
+        "//jax:experimental_array_api",
+    ] + py_deps("absl/testing"),
+)
+
 jax_test(
     name = "array_interoperability_test",
     srcs = ["array_interoperability_test.py"],
diff --git a/tests/array_api_test.py b/tests/array_api_test.py
new file mode 100644
index 000000000000..97fc682398e4
--- /dev/null
+++ b/tests/array_api_test.py
@@ -0,0 +1,238 @@
+# Copyright 2023 The JAX Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Smoketest for jax.experimental.array_api
+
+The full test suite for the array API is run via the array-api-tests CI;
+this is just a minimal smoke test to catch issues early.
+"""
+from __future__ import annotations
+
+from types import ModuleType
+
+from absl.testing import absltest
+import jax
+from jax import config
+from jax.experimental import array_api
+
+config.parse_flags_with_absl()
+
+MAIN_NAMESPACE = {
+  'abs',
+  'acos',
+  'acosh',
+  'add',
+  'all',
+  'annotations',
+  'any',
+  'arange',
+  'argmax',
+  'argmin',
+  'argsort',
+  'asarray',
+  'asin',
+  'asinh',
+  'astype',
+  'atan',
+  'atan2',
+  'atanh',
+  'bitwise_and',
+  'bitwise_invert',
+  'bitwise_left_shift',
+  'bitwise_or',
+  'bitwise_right_shift',
+  'bitwise_xor',
+  'bool',
+  'broadcast_arrays',
+  'broadcast_to',
+  'can_cast',
+  'ceil',
+  'complex128',
+  'complex64',
+  'concat',
+  'conj',
+  'cos',
+  'cosh',
+  'divide',
+  'e',
+  'empty',
+  'empty_like',
+  'equal',
+  'exp',
+  'expand_dims',
+  'expm1',
+  'eye',
+  'fft',
+  'finfo',
+  'flip',
+  'float32',
+  'float64',
+  'floor',
+  'floor_divide',
+  'from_dlpack',
+  'full',
+  'full_like',
+  'greater',
+  'greater_equal',
+  'iinfo',
+  'imag',
+  'inf',
+  'int16',
+  'int32',
+  'int64',
+  'int8',
+  'isdtype',
+  'isfinite',
+  'isinf',
+  'isnan',
+  'less',
+  'less_equal',
+  'linalg',
+  'linspace',
+  'log',
+  'log10',
+  'log1p',
+  'log2',
+  'logaddexp',
+  'logical_and',
+  'logical_not',
+  'logical_or',
+  'logical_xor',
+  'matmul',
+  'matrix_transpose',
+  'max',
+  'mean',
+  'meshgrid',
+  'min',
+  'multiply',
+  'nan',
+  'negative',
+  'newaxis',
+  'nonzero',
+  'not_equal',
+  'ones',
+  'ones_like',
+  'permute_dims',
+  'pi',
+  'positive',
+  'pow',
+  'prod',
+  'real',
+  'remainder',
+  'reshape',
+  'result_type',
+  'roll',
+  'round',
+  'sign',
+  'sin',
+  'sinh',
+  'sort',
+  'sqrt',
+  'square',
+  'squeeze',
+  'stack',
+  'std',
+  'subtract',
+  'sum',
+  'take',
+  'tan',
+  'tanh',
+  'tensordot',
+  'tril',
+  'triu',
+  'trunc',
+  'uint16',
+  'uint32',
+  'uint64',
+  'uint8',
+  'unique_all',
+  'unique_counts',
+  'unique_inverse',
+  'unique_values',
+  'var',
+  'vecdot',
+  'where',
+  'zeros',
+  'zeros_like',
+}
+
+LINALG_NAMESPACE = {
+  'cholesky',
+  'cross',
+  'det',
+  'diagonal',
+  'eigh',
+  'eigvalsh',
+  'inv',
+  'jax',
+  'matmul',
+  'matrix_norm',
+  'matrix_power',
+  'matrix_rank',
+  'matrix_transpose',
+  'outer',
+  'pinv',
+  'qr',
+  'slogdet',
+  'solve',
+  'svd',
+  'svdvals',
+  'tensordot',
+  'trace',
+  'vecdot',
+  'vector_norm',
+}
+
+FFT_NAMESPACE = {
+  'fft',
+  'fftfreq',
+  'fftn',
+  'fftshift',
+  'hfft',
+  'ifft',
+  'ifftn',
+  'ifftshift',
+  'ihfft',
+  'irfft',
+  'irfftn',
+  'rfft',
+  'rfftfreq',
+  'rfftn',
+}
+
+
+def names(module: ModuleType) -> set[str]:
+  return {name for name in dir(module) if not name.startswith('_')}
+
+
+class ArrayAPISmokeTest(absltest.TestCase):
+  """Smoke test for the array API."""
+
+  def test_main_namespace(self):
+    self.assertSetEqual(names(array_api), MAIN_NAMESPACE)
+
+  def test_linalg_namespace(self):
+    self.assertSetEqual(names(array_api.linalg), LINALG_NAMESPACE)
+
+  def test_fft_namespace(self):
+    self.assertSetEqual(names(array_api.fft), FFT_NAMESPACE)
+
+  def test_array_namespace_method(self):
+    x = array_api.arange(20)
+    self.assertIsInstance(x, jax.Array)
+    self.assertIs(x.__array_namespace__(), array_api)
+
+
+if __name__ == '__main__':
+  absltest.main()