diff --git a/.changelog/5512.changed b/.changelog/5512.changed
new file mode 100644
index 00000000000..f09b7517279
--- /dev/null
+++ b/.changelog/5512.changed
@@ -0,0 +1 @@
+`opentelemetry-sdk`: `SimpleSpanProcessor` now drops spans ended after `shutdown()` instead of passing them to the exporter, and counts them on `otel.sdk.processor.span.processed` with `error.type=already_shutdown`.
diff --git a/opentelemetry-sdk/src/opentelemetry/sdk/trace/export/__init__.py b/opentelemetry-sdk/src/opentelemetry/sdk/trace/export/__init__.py
index 82ffbd0b0cb..525334173d8 100644
--- a/opentelemetry-sdk/src/opentelemetry/sdk/trace/export/__init__.py
+++ b/opentelemetry-sdk/src/opentelemetry/sdk/trace/export/__init__.py
@@ -99,6 +99,7 @@ def __init__(
         meter_provider: MeterProvider | None = None,
     ):
         self.span_exporter = span_exporter
+        self._shutdown = False
         self._metrics = create_processor_metrics(
             "traces",
             OtelComponentTypeValues.SIMPLE_SPAN_PROCESSOR,
@@ -115,6 +116,10 @@ def _on_ending(self, span: Span) -> None:
     def on_end(self, span: ReadableSpan) -> None:
         if not (span.context and span.context.trace_flags.sampled):
             return
+        if self._shutdown:
+            logger.warning("Processor is already shutdown, ignoring call")
+            self._metrics.drop_items(1, "already_shutdown")
+            return
         token = attach(set_value(_SUPPRESS_INSTRUMENTATION_KEY, True))
         # Record on submission to the exporter.
         self._metrics.finish_items(1)
@@ -127,6 +132,7 @@ def on_end(self, span: ReadableSpan) -> None:
             detach(token)
 
     def shutdown(self) -> None:
+        self._shutdown = True
         self.span_exporter.shutdown()
 
     def force_flush(self, timeout_millis: int = 30000) -> bool:
diff --git a/opentelemetry-sdk/tests/trace/export/test_export.py b/opentelemetry-sdk/tests/trace/export/test_export.py
index 55345c89903..6f7a303ae04 100644
--- a/opentelemetry-sdk/tests/trace/export/test_export.py
+++ b/opentelemetry-sdk/tests/trace/export/test_export.py
@@ -174,6 +174,44 @@ def export_spans(_spans):
         self.assertTrue(processed_data_point0.attributes["otel.component.name"].startswith("simple_span_processor/"))
         self.assertIsNone(processed_data_point0.attributes.get("error.type"))
 
+    @mock.patch.dict("os.environ", {OTEL_PYTHON_SDK_INTERNAL_METRICS_ENABLED: "true"})
+    def test_metrics_already_shutdown(self):
+        metric_reader = InMemoryMetricReader()
+        meter_provider = MeterProvider(metric_readers=[metric_reader])
+
+        exporter = mock.MagicMock()
+        exporter.export.return_value = export.SpanExportResult.SUCCESS
+        span_processor = export.SimpleSpanProcessor(exporter, meter_provider=meter_provider)
+        provider = trace.TracerProvider()
+        tracer = provider.get_tracer(__name__)
+        provider.add_span_processor(span_processor)
+
+        # Ended before shutdown: submitted to the exporter and counted as
+        # successfully processed.
+        with tracer.start_as_current_span("foo"):
+            pass
+        span_processor.shutdown()
+
+        # Ended after shutdown: dropped and counted as already_shutdown.
+        with tracer.start_as_current_span("bar"):
+            pass
+
+        metrics_data = metric_reader.get_metrics_data()
+        scope_metrics = metrics_data.resource_metrics[0].scope_metrics[0]
+        processed = next(m for m in scope_metrics.metrics if m.name == "otel.sdk.processor.span.processed")
+        data_points = sorted(
+            processed.data.data_points,
+            key=lambda dp: dp.attributes.get("error.type", ""),
+        )
+        self.assertEqual(len(data_points), 2)
+        self.assertEqual(data_points[0].value, 1)
+        self.assertIsNone(data_points[0].attributes.get("error.type"))
+        self.assertEqual(data_points[1].value, 1)
+        self.assertEqual(data_points[1].attributes.get("error.type"), "already_shutdown")
+        # Only the pre-shutdown span is submitted to the exporter; the
+        # post-shutdown span is dropped, not exported.
+        self.assertEqual(exporter.export.call_count, 1)
+
 
 # Many more test cases for the BatchSpanProcessor exist under
 # opentelemetry-sdk/tests/shared_internal/test_batch_processor.py.