diff --git a/src/shims/time.rs b/src/shims/time.rs
index a2cbd84bc2d..d9edbe3d7bd 100644
--- a/src/shims/time.rs
+++ b/src/shims/time.rs
@@ -210,7 +210,11 @@ fn nanosleep(
                 return Ok(-1);
             }
         };
-        let timeout_time = Time::Monotonic(Instant::now().checked_add(duration).unwrap());
+        // If adding the duration overflows, let's just sleep for an hour. Waking up early is always acceptable.
+        let timeout_time = Instant::now()
+            .checked_add(duration)
+            .unwrap_or_else(|| Instant::now().checked_add(Duration::from_secs(3600)).unwrap());
+        let timeout_time = Time::Monotonic(timeout_time);
 
         let active_thread = this.get_active_thread();
         this.block_thread(active_thread);
diff --git a/tests/pass/sleep_long.rs b/tests/pass/sleep_long.rs
new file mode 100644
index 00000000000..dd4a1843942
--- /dev/null
+++ b/tests/pass/sleep_long.rs
@@ -0,0 +1,18 @@
+//@ignore-target-windows: no threads nor sleep on Windows
+//@compile-flags: -Zmiri-ignore-leaks -Zmiri-disable-isolation
+use std::sync::{Arc, Mutex};
+use std::thread;
+use std::time::Duration;
+
+fn main() {
+    let finished = Arc::new(Mutex::new(false));
+    let t_finished = finished.clone();
+    thread::spawn(move || {
+        // Sleep very, very long.
+        thread::sleep(Duration::new(u64::MAX, 0));
+        *t_finished.lock().unwrap() = true;
+    });
+    thread::sleep(Duration::from_millis(100));
+    assert_eq!(*finished.lock().unwrap(), false);
+    // Stopping the main thread will also kill the sleeper.
+}