diff --git a/implementations/micrometer-registry-statsd/src/main/java/io/micrometer/statsd/StatsdMeterRegistry.java b/implementations/micrometer-registry-statsd/src/main/java/io/micrometer/statsd/StatsdMeterRegistry.java
index a1843cbe25..a57585e98b 100644
--- a/implementations/micrometer-registry-statsd/src/main/java/io/micrometer/statsd/StatsdMeterRegistry.java
+++ b/implementations/micrometer-registry-statsd/src/main/java/io/micrometer/statsd/StatsdMeterRegistry.java
@@ -175,7 +175,11 @@ private <M extends Meter> void removePollableMeter(M m) {
 
     void poll() {
         for (StatsdPollable pollableMeter : pollableMeters.values()) {
-            pollableMeter.poll();
+            try {
+                pollableMeter.poll();
+            } catch (RuntimeException e) {
+                // Silently ignore misbehaving pollable meter
+            }
         }
     }
 
diff --git a/implementations/micrometer-registry-statsd/src/test/java/io/micrometer/statsd/StatsdMeterRegistryTest.java b/implementations/micrometer-registry-statsd/src/test/java/io/micrometer/statsd/StatsdMeterRegistryTest.java
index 77c5fcf2d8..629b4d652f 100644
--- a/implementations/micrometer-registry-statsd/src/test/java/io/micrometer/statsd/StatsdMeterRegistryTest.java
+++ b/implementations/micrometer-registry-statsd/src/test/java/io/micrometer/statsd/StatsdMeterRegistryTest.java
@@ -45,8 +45,7 @@
 
 import static java.util.Collections.singletonList;
 import static java.util.stream.IntStream.range;
-import static org.assertj.core.api.Assertions.assertThat;
-import static org.assertj.core.api.Assertions.fail;
+import static org.assertj.core.api.Assertions.*;
 
 /**
  * Tests for {@link StatsdMeterRegistry}.
@@ -544,6 +543,17 @@ void stopTrackingMetersThatAreRemoved() {
         assertThat(lines.get("functioncounter")).isEqualTo(1);
     }
 
+    @Test
+    void pollFailureNotFatal() {
+        registry = StatsdMeterRegistry.builder(StatsdConfig.DEFAULT).build();
+        Gauge.builder("fails", "", o -> {
+            throw new RuntimeException();
+        }).register(registry);
+        Gauge.builder("works", () -> 42).register(registry);
+
+        assertThatCode(() -> registry.poll()).doesNotThrowAnyException();
+    }
+
     @Test
     @Issue("#2064")
     void publishLongTaskTimerMax() throws InterruptedException {