diff --git a/compiler/rustc_mir_build/src/thir/pattern/check_match.rs b/compiler/rustc_mir_build/src/thir/pattern/check_match.rs
index f46cf0dc0ff..cce2a8c5259 100644
--- a/compiler/rustc_mir_build/src/thir/pattern/check_match.rs
+++ b/compiler/rustc_mir_build/src/thir/pattern/check_match.rs
@@ -735,17 +735,21 @@ fn non_exhaustive_match<'p, 'tcx>(
         collect_non_exhaustive_tys(&witnesses[0], &mut non_exhaustive_tys);
 
         for ty in non_exhaustive_tys {
-            if ty == cx.tcx.types.usize || ty == cx.tcx.types.isize {
+            if ty.is_ptr_sized_integral() {
                 err.note(format!(
                     "`{ty}` does not have a fixed maximum value, so a wildcard `_` is necessary to match \
-                     exhaustively",
-                ));
+                         exhaustively",
+                    ));
                 if cx.tcx.sess.is_nightly_build() {
                     err.help(format!(
-                        "add `#![feature(precise_pointer_size_matching)]` to the crate attributes to \
-                         enable precise `{ty}` matching",
-                    ));
+                            "add `#![feature(precise_pointer_size_matching)]` to the crate attributes to \
+                             enable precise `{ty}` matching",
+                        ));
                 }
+            } else if ty == cx.tcx.types.str_ {
+                err.note(format!(
+                    "`{ty}` cannot be matched exhaustively, so a wildcard `_` is necessary",
+                ));
             }
         }
     }
diff --git a/tests/ui/pattern/usefulness/issue-105479-str-non-exhaustiveness.rs b/tests/ui/pattern/usefulness/issue-105479-str-non-exhaustiveness.rs
new file mode 100644
index 00000000000..faf37b07513
--- /dev/null
+++ b/tests/ui/pattern/usefulness/issue-105479-str-non-exhaustiveness.rs
@@ -0,0 +1,12 @@
+fn main() {
+    let a = "";
+    let b = "";
+    match (a, b) {
+        //~^ ERROR non-exhaustive patterns: `(&_, _)` not covered [E0004]
+        //~| NOTE pattern `(&_, _)` not covered
+        //~| NOTE the matched value is of type `(&str, &str)`
+        //~| NOTE `str` cannot be matched exhaustively, so a wildcard `_` is necessary
+        ("a", "b") => {}
+        ("c", "d") => {}
+    }
+}
diff --git a/tests/ui/pattern/usefulness/issue-105479-str-non-exhaustiveness.stderr b/tests/ui/pattern/usefulness/issue-105479-str-non-exhaustiveness.stderr
new file mode 100644
index 00000000000..5c09b3bada6
--- /dev/null
+++ b/tests/ui/pattern/usefulness/issue-105479-str-non-exhaustiveness.stderr
@@ -0,0 +1,17 @@
+error[E0004]: non-exhaustive patterns: `(&_, _)` not covered
+  --> $DIR/issue-105479-str-non-exhaustiveness.rs:4:11
+   |
+LL |     match (a, b) {
+   |           ^^^^^^ pattern `(&_, _)` not covered
+   |
+   = note: the matched value is of type `(&str, &str)`
+   = note: `str` cannot be matched exhaustively, so a wildcard `_` is necessary
+help: ensure that all possible cases are being handled by adding a match arm with a wildcard pattern or an explicit pattern as shown
+   |
+LL ~         ("c", "d") => {},
+LL +         (&_, _) => todo!()
+   |
+
+error: aborting due to previous error
+
+For more information about this error, try `rustc --explain E0004`.
diff --git a/tests/ui/pattern/usefulness/issue-30240.stderr b/tests/ui/pattern/usefulness/issue-30240.stderr
index ff755d681ac..736ab34e164 100644
--- a/tests/ui/pattern/usefulness/issue-30240.stderr
+++ b/tests/ui/pattern/usefulness/issue-30240.stderr
@@ -5,6 +5,7 @@ LL |     match "world" {
    |           ^^^^^^^ pattern `&_` not covered
    |
    = note: the matched value is of type `&str`
+   = note: `str` cannot be matched exhaustively, so a wildcard `_` is necessary
 help: ensure that all possible cases are being handled by adding a match arm with a wildcard pattern or an explicit pattern as shown
    |
 LL ~         "hello" => {},
@@ -18,6 +19,7 @@ LL |     match "world" {
    |           ^^^^^^^ pattern `&_` not covered
    |
    = note: the matched value is of type `&str`
+   = note: `str` cannot be matched exhaustively, so a wildcard `_` is necessary
 help: ensure that all possible cases are being handled by adding a match arm with a wildcard pattern or an explicit pattern as shown
    |
 LL ~         "hello" => {},