diff --git a/src/naive/date.rs b/src/naive/date.rs
index a174cae84..f23e159b1 100644
--- a/src/naive/date.rs
+++ b/src/naive/date.rs
@@ -79,10 +79,13 @@ impl NaiveWeek {
     #[inline]
     #[must_use]
     pub fn first_day(&self) -> NaiveDate {
-        let start = self.start.num_days_from_monday();
-        let end = self.date.weekday().num_days_from_monday();
-        let days = if start > end { 7 - start + end } else { end - start };
-        self.date - Duration::days(days.into())
+        let start = self.start.num_days_from_monday() as i32;
+        let ref_day = self.date.weekday().num_days_from_monday() as i32;
+        // Calculate the number of days to subtract from `self.date`.
+        // Do not construct an intermediate date beyond `self.date`, because that may be out of
+        // range if `date` is close to `NaiveDate::MAX`.
+        let days = start - ref_day - if start > ref_day { 7 } else { 0 };
+        self.date.diff_days(days as i64).unwrap()
     }
 
     /// Returns a date representing the last day of the week.
@@ -99,7 +102,13 @@ impl NaiveWeek {
     #[inline]
     #[must_use]
     pub fn last_day(&self) -> NaiveDate {
-        self.first_day() + Duration::days(6)
+        let end = self.start.pred().num_days_from_monday() as i32;
+        let ref_day = self.date.weekday().num_days_from_monday() as i32;
+        // Calculate the number of days to add to `self.date`.
+        // Do not construct an intermediate date before `self.date` (like with `first_day()`),
+        // because that may be out of range if `date` is close to `NaiveDate::MIN`.
+        let days = end - ref_day + if end < ref_day { 7 } else { 0 };
+        self.date.diff_days(days as i64).unwrap()
     }
 
     /// Returns a [`RangeInclusive<T>`] representing the whole week bounded by
@@ -3019,23 +3028,31 @@ mod tests {
     fn test_naiveweek() {
         let date = NaiveDate::from_ymd_opt(2022, 5, 18).unwrap();
         let asserts = vec![
-            (Weekday::Mon, "2022-05-16", "2022-05-22"),
-            (Weekday::Tue, "2022-05-17", "2022-05-23"),
-            (Weekday::Wed, "2022-05-18", "2022-05-24"),
-            (Weekday::Thu, "2022-05-12", "2022-05-18"),
-            (Weekday::Fri, "2022-05-13", "2022-05-19"),
-            (Weekday::Sat, "2022-05-14", "2022-05-20"),
-            (Weekday::Sun, "2022-05-15", "2022-05-21"),
+            (Weekday::Mon, "Mon 2022-05-16", "Sun 2022-05-22"),
+            (Weekday::Tue, "Tue 2022-05-17", "Mon 2022-05-23"),
+            (Weekday::Wed, "Wed 2022-05-18", "Tue 2022-05-24"),
+            (Weekday::Thu, "Thu 2022-05-12", "Wed 2022-05-18"),
+            (Weekday::Fri, "Fri 2022-05-13", "Thu 2022-05-19"),
+            (Weekday::Sat, "Sat 2022-05-14", "Fri 2022-05-20"),
+            (Weekday::Sun, "Sun 2022-05-15", "Sat 2022-05-21"),
         ];
         for (start, first_day, last_day) in asserts {
             let week = date.week(start);
             let days = week.days();
-            assert_eq!(Ok(week.first_day()), NaiveDate::parse_from_str(first_day, "%Y-%m-%d"));
-            assert_eq!(Ok(week.last_day()), NaiveDate::parse_from_str(last_day, "%Y-%m-%d"));
+            assert_eq!(Ok(week.first_day()), NaiveDate::parse_from_str(first_day, "%a %Y-%m-%d"));
+            assert_eq!(Ok(week.last_day()), NaiveDate::parse_from_str(last_day, "%a %Y-%m-%d"));
             assert!(days.contains(&date));
         }
     }
 
+    #[test]
+    fn test_naiveweek_min_max() {
+        let date_max = NaiveDate::MAX;
+        assert!(date_max.week(Weekday::Mon).first_day() <= date_max);
+        let date_min = NaiveDate::MIN;
+        assert!(date_min.week(Weekday::Mon).last_day() >= date_min);
+    }
+
     #[test]
     fn test_weeks_from() {
         // tests per: https://github.com/chronotope/chrono/issues/961