diff --git a/python/ray/tune/sample.py b/python/ray/tune/sample.py
index 4a2180b5d..e4d349ee9 100644
--- a/python/ray/tune/sample.py
+++ b/python/ray/tune/sample.py
@@ -333,8 +333,7 @@ class Function(Domain):
                    domain: "Function",
                    spec: Optional[Union[List[Dict], Dict]] = None,
                    size: int = 1):
-            pass_spec = len(signature(domain.func).parameters) > 0
-            if pass_spec:
+            if domain.pass_spec:
                 items = [
                     domain.func(spec[i] if isinstance(spec, list) else spec)
                     for i in range(size)
@@ -347,11 +346,23 @@ class Function(Domain):
     default_sampler_cls = _CallSampler
 
     def __init__(self, func: Callable):
-        if len(signature(func).parameters) > 1:
-            raise ValueError(
-                "The function passed to a `Function` parameter must accept "
-                "either 0 or 1 parameters.")
+        sig = signature(func)
 
+        pass_spec = True  # whether we should pass `spec` when calling `func`
+        try:
+            sig.bind({})
+        except TypeError:
+            pass_spec = False
+
+        if not pass_spec:
+            try:
+                sig.bind()
+            except TypeError as exc:
+                raise ValueError(
+                    "The function passed to a `Function` parameter must be "
+                    "callable with either 0 or 1 parameters.") from exc
+
+        self.pass_spec = pass_spec
         self.func = func
 
     def is_function(self):
diff --git a/python/ray/tune/tests/test_sample.py b/python/ray/tune/tests/test_sample.py
index 4c1d1a1cb..1b6821439 100644
--- a/python/ray/tune/tests/test_sample.py
+++ b/python/ray/tune/tests/test_sample.py
@@ -142,6 +142,32 @@ class SearchSpaceTest(unittest.TestCase):
         self.assertTrue(any(-4 < s < 4 for s in samples))
         self.assertTrue(-2 < np.mean(samples) < 2)
 
+    def testFunctionSignature(self):
+        from functools import partial
+
+        def sample_a():
+            return 0
+
+        def sample_b(spec):
+            return 1
+
+        def sample_c(spec, b="ok"):
+            return 2
+
+        def sample_d_invalid(spec, b):
+            return 3
+
+        sample_d_valid = partial(sample_d_invalid, b="ok")
+
+        for sample_fn in [sample_a, sample_b, sample_c, sample_d_valid]:
+            fn = tune.sample_from(sample_fn)
+            sample = fn.sample(None)
+            self.assertIsNotNone(sample)
+
+        with self.assertRaises(ValueError):
+            fn = tune.sample_from(sample_d_invalid)
+            print(fn.sample(None))
+
     def testQuantized(self):
         bounded_positive = tune.sample.Float(1e-4, 1e-1)