diff --git a/sentry_sdk/client.py b/sentry_sdk/client.py
index 0f2ddfb640..07ac164e80 100644
--- a/sentry_sdk/client.py
+++ b/sentry_sdk/client.py
@@ -507,6 +507,14 @@ def _setup_instrumentation(
         for function in functions_to_trace:
             class_name = None
             function_qualname = function["qualified_name"]
+
+            if "." not in function_qualname:
+                logger.warning(
+                    "Can not enable tracing for '%s'. Please provide the fully qualified name including the module (e.g. 'mymodule.my_function').",
+                    function_qualname,
+                )
+                continue
+
             module_name, function_name = function_qualname.rsplit(".", 1)
 
             try:
diff --git a/tests/test_basics.py b/tests/test_basics.py
index f628d139d1..01d518eee6 100644
--- a/tests/test_basics.py
+++ b/tests/test_basics.py
@@ -1090,6 +1090,14 @@ def test_classmethod_instance_tracing(sentry_init, capture_events):
     assert span["description"] == "tests.test_basics.TracingTestClass.class_"
 
 
+def test_functions_to_trace_no_dot_does_not_crash(sentry_init):
+    # A qualified_name with no dot should not raise ValueError during sentry_sdk.init()
+    sentry_init(
+        traces_sample_rate=1.0,
+        functions_to_trace=[{"qualified_name": "my_function"}],
+    )
+
+
 def test_last_event_id(sentry_init):
     sentry_init(traces_sample_rate=1.0)