diff --git a/CHANGELOG.md b/CHANGELOG.md
index 1cfecebadd..fd8facd028 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -20,6 +20,7 @@ Versions with only mechanical changes will be omitted from the following list.
 * Add `DateTime::from_local()` to construct from given local date and time (#572)
 * Correct build for wasm32-unknown-emscripten target (#568)
 * Change `Local::now()` and `Utc::now()` documentation from "current date" to "current date and time" (#647)
+* Fix `duration_round` panic on rounding by `Duration::zero()` (#658)
 
 ## 0.4.19
 
diff --git a/src/round.rs b/src/round.rs
index b357d916c0..c10b78c760 100644
--- a/src/round.rs
+++ b/src/round.rs
@@ -185,6 +185,9 @@ where
         if span > stamp.abs() {
             return Err(RoundingError::DurationExceedsTimestamp);
         }
+        if span == 0 {
+            return Ok(original);
+        }
         let delta_down = stamp % span;
         if delta_down == 0 {
             Ok(original)
@@ -394,6 +397,11 @@ mod tests {
     fn test_duration_round() {
         let dt = Utc.ymd(2016, 12, 31).and_hms_nano(23, 59, 59, 175_500_000);
 
+        assert_eq!(
+            dt.duration_round(Duration::zero()).unwrap().to_string(),
+            "2016-12-31 23:59:59.175500 UTC"
+        );
+
         assert_eq!(
             dt.duration_round(Duration::milliseconds(10)).unwrap().to_string(),
             "2016-12-31 23:59:59.180 UTC"
@@ -456,6 +464,11 @@ mod tests {
     fn test_duration_round_naive() {
         let dt = Utc.ymd(2016, 12, 31).and_hms_nano(23, 59, 59, 175_500_000).naive_utc();
 
+        assert_eq!(
+            dt.duration_round(Duration::zero()).unwrap().to_string(),
+            "2016-12-31 23:59:59.175500"
+        );
+
         assert_eq!(
             dt.duration_round(Duration::milliseconds(10)).unwrap().to_string(),
             "2016-12-31 23:59:59.180"