diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4de8ce8c86..eaa4da4d2c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,11 @@
 # Changelog
 
+## Unreleased
+
+### Fixes
+
+- When using OTel and ASP.NET Core the SDK could try to process OTel spans after the SDK had been closed ([#3726](https://github.com/getsentry/sentry-dotnet/pull/3726))
+
 ## 4.12.2
 
 ### Features
diff --git a/src/Sentry.OpenTelemetry/SentrySpanProcessor.cs b/src/Sentry.OpenTelemetry/SentrySpanProcessor.cs
index c34415caf5..9f32987db5 100644
--- a/src/Sentry.OpenTelemetry/SentrySpanProcessor.cs
+++ b/src/Sentry.OpenTelemetry/SentrySpanProcessor.cs
@@ -83,6 +83,14 @@ internal SentrySpanProcessor(IHub hub, IEnumerable<IOpenTelemetryEnricher>? enri
     /// <inheritdoc />
     public override void OnStart(Activity data)
     {
+        if (!_hub.IsEnabled)
+        {
+            // This would be unusual... it might happen if the SDK is closed while the processor is still running and
+            // we receive new telemetry. In this case, we can't log anything because our logger is disabled, so we just
+            // swallow it
+            return;
+        }
+
         if (data.ParentSpanId != default && _map.TryGetValue(data.ParentSpanId, out var mappedParent))
         {
             // Explicit ParentSpanId of another activity that we have already mapped
@@ -165,6 +173,14 @@ private void CreateRootSpan(Activity data)
     /// <inheritdoc />
     public override void OnEnd(Activity data)
     {
+        if (!_hub.IsEnabled)
+        {
+            // This would be unusual... it might happen if the SDK is closed while the processor is still running and
+            // we receive new telemetry. In this case, we can't log anything because our logger is disabled, so we just
+            // swallow it
+            return;
+        }
+
         // Make a dictionary of the attributes (aka "tags") for faster lookup when used throughout the processor.
         var attributes = data.TagObjects.ToDict();
 
diff --git a/test/Sentry.OpenTelemetry.Tests/SentrySpanProcessorTests.cs b/test/Sentry.OpenTelemetry.Tests/SentrySpanProcessorTests.cs
index 7ee5b0de0e..92839b2f56 100644
--- a/test/Sentry.OpenTelemetry.Tests/SentrySpanProcessorTests.cs
+++ b/test/Sentry.OpenTelemetry.Tests/SentrySpanProcessorTests.cs
@@ -34,9 +34,9 @@ public Fixture()
 
         public Hub GetHub() => Hub ??= new Hub(Options, Client, SessionManager, Clock, ScopeManager);
 
-        public SentrySpanProcessor GetSut()
+        public SentrySpanProcessor GetSut(IHub hub = null)
         {
-            return new SentrySpanProcessor(GetHub(), Enrichers);
+            return new SentrySpanProcessor(hub ?? GetHub(), Enrichers);
         }
     }
 
@@ -488,6 +488,54 @@ public void OnEnd_IsSentryRequest_DoesNotFinishTransaction(string urlKey)
         transaction.IsSentryRequest.Should().BeTrue();
     }
 
+    [Fact]
+    public void OnStart_DisabledHub_DoesNothing()
+    {
+        // Arrange
+        _fixture.Options.Instrumenter = Instrumenter.OpenTelemetry;
+        SentryClientExtensions.SentryOptionsForTestingOnly = _fixture.Options;
+        var hub = Substitute.For<IHub>();
+        hub.IsEnabled.Returns(false);
+        var sut = _fixture.GetSut(hub);
+
+        var data = Tracer.StartActivity()!;
+
+        // Act
+        sut.OnStart(data);
+
+        // Assert
+        sut._map.Should().BeEmpty();
+        hub.Received(0).GetSpan();
+        hub.Received(0).StartTransaction(
+            Arg.Any<ITransactionContext>(),
+            Arg.Any<IReadOnlyDictionary<string, object>>()
+            );
+    }
+
+    [Fact]
+    public void OnEnd_DisabledHub_DoesNothing()
+    {
+        // Arrange
+        _fixture.Options.Instrumenter = Instrumenter.OpenTelemetry;
+        SentryClientExtensions.SentryOptionsForTestingOnly = _fixture.Options;
+        var hub = Substitute.For<IHub>();
+        hub.IsEnabled.Returns(true, false);
+        var sut = _fixture.GetSut(hub);
+
+        var data = Tracer.StartActivity()!;
+
+        // Act
+        sut.OnEnd(data);
+
+        // Assert
+        sut._map.Should().BeEmpty();
+        hub.Received(0).GetSpan();
+        hub.Received(0).StartTransaction(
+            Arg.Any<ITransactionContext>(),
+            Arg.Any<IReadOnlyDictionary<string, object>>()
+        );
+    }
+
     private static void FilterActivity(Activity activity)
     {
         // Simulates filtering an activity - see https://github.com/getsentry/sentry-dotnet/pull/3198