diff --git a/tokio/src/time/interval.rs b/tokio/src/time/interval.rs
index 0153a567f10..2af1e49fbed 100644
--- a/tokio/src/time/interval.rs
+++ b/tokio/src/time/interval.rs
@@ -340,10 +340,12 @@ impl MissedTickBehavior {
     /// If a tick is missed, this method is called to determine when the next tick should happen.
     fn next_timeout(&self, timeout: Instant, now: Instant, period: Duration) -> Instant {
         match self {
-            Self::Burst => timeout + period,
-            Self::Delay => now + period,
+            Self::Burst => timeout
+                .checked_add(period)
+                .unwrap_or_else(Instant::far_future),
+            Self::Delay => now.checked_add(period).unwrap_or_else(Instant::far_future),
             Self::Skip => {
-                now + period
+                now.checked_add(period).unwrap_or_else(Instant::far_future)
                     - Duration::from_nanos(
                         ((now - timeout).as_nanos() % period.as_nanos())
                             .try_into()
@@ -475,7 +477,8 @@ impl Interval {
         // However, if a tick took excessively long and we are now behind,
         // schedule the next tick according to how the user specified with
         // `MissedTickBehavior`
-        let next = if now > timeout + Duration::from_millis(5) {
+
+        let next = if now.saturating_duration_since(timeout) > Duration::from_millis(5) {
             self.missed_tick_behavior
                 .next_timeout(timeout, now, self.period)
         } else {
diff --git a/tokio/tests/time_interval.rs b/tokio/tests/time_interval.rs
index 7472a37123c..71a83567966 100644
--- a/tokio/tests/time_interval.rs
+++ b/tokio/tests/time_interval.rs
@@ -470,8 +470,25 @@ async fn stream_with_interval_poll_tick_no_waking() {
     assert_eq!(items, vec![]);
 }
 
-#[tokio::test(start_paused = true)]
+#[tokio::test]
 async fn interval_doesnt_panic_max_duration_when_polling() {
-    let mut timer = task::spawn(time::interval(Duration::MAX));
+    let mut timer = task::spawn(time::interval(Duration::from_secs(u64::MAX)));
+
+    // The `Interval::delay` is not ready yet.
+    let result = timer.enter(|cx, mut timer| timer.poll_tick(cx));
+    assert!(result.is_pending());
+
+    // Sleep 1 second to ensure we capture a missed tick.
+    tokio::time::sleep(tokio::time::Duration::from_secs(1)).await;
+
+    // Call the poll tick again to check the duration doesn't panic.
+    // These 2 polls are equivalent to `timer.tick().await` that disarm the first interval fire.
     assert_ready!(timer.enter(|cx, mut timer| timer.poll_tick(cx)));
+
+    // Sleep again.
+    tokio::time::sleep(tokio::time::Duration::from_secs(1)).await;
+
+    // This time we expect the timer to fire at the specified interval (ie too far in the future).
+    let result = timer.enter(|cx, mut timer| timer.poll_tick(cx));
+    assert!(result.is_pending());
 }