diff --git a/tests/by-util/test_env.rs b/tests/by-util/test_env.rs
index ecb215f8c..0d9d94b01 100644
--- a/tests/by-util/test_env.rs
+++ b/tests/by-util/test_env.rs
@@ -1,4 +1,4 @@
-// spell-checker:ignore (words) bamf chdir
+// spell-checker:ignore (words) bamf chdir rlimit prlimit
 
 #[cfg(not(windows))]
 use std::fs;
@@ -80,6 +80,20 @@ fn test_combined_file_set_unset() {
     );
 }
 
+#[test]
+fn test_unset_invalid_variables() {
+    use uucore::display::Quotable;
+
+    // Cannot test input with \0 in it, since output will also contain \0. rlimit::prlimit fails
+    // with this error: Error { kind: InvalidInput, message: "nul byte found in provided data" }
+    for var in &["", "a=b"] {
+        new_ucmd!().arg("-u").arg(var).run().stderr_only(format!(
+            "env: cannot unset {}: Invalid argument",
+            var.quote()
+        ));
+    }
+}
+
 #[test]
 fn test_single_name_value_pair() {
     let out = new_ucmd!().arg("FOO=bar").run();