diff --git a/lang/rust/avro/src/schema.rs b/lang/rust/avro/src/schema.rs
index d2858722bd6..47900e46be3 100644
--- a/lang/rust/avro/src/schema.rs
+++ b/lang/rust/avro/src/schema.rs
@@ -42,7 +42,7 @@ lazy_static! {
 
     // An optional namespace (with optional dots) followed by a name without any dots in it.
     static ref SCHEMA_NAME_R: Regex =
-        Regex::new(r"^((?P<namespace>([A-Za-z_][A-Za-z0-9_\.]*)*)\.)?(?P<name>[A-Za-z_][A-Za-z0-9_]*)$").unwrap();
+        Regex::new(r"^((?P<namespace>([A-Za-z_][A-Za-z0-9_]*(\.[A-Za-z_][A-Za-z0-9_]*)*)?)\.)?(?P<name>[A-Za-z_][A-Za-z0-9_]*)$").unwrap();
 
     static ref FIELD_NAME_R: Regex = Regex::new(r"^[A-Za-z_][A-Za-z0-9_]*$").unwrap();
 
@@ -6195,4 +6195,37 @@ mod tests {
 
         Ok(())
     }
+
+    #[test]
+    fn test_avro_3897_disallow_invalid_namespaces_in_fully_qualified_name() -> TestResult {
+        let full_name = "ns.0.record1";
+        let name = Name::new(full_name);
+        assert!(name.is_err());
+        let expected =
+            Error::InvalidSchemaName(full_name.to_string(), SCHEMA_NAME_R.as_str()).to_string();
+        let err = name.map_err(|e| e.to_string()).err().unwrap();
+        assert_eq!(expected, err);
+
+        let full_name = "ns..record1";
+        let name = Name::new(full_name);
+        assert!(name.is_err());
+        let expected =
+            Error::InvalidSchemaName(full_name.to_string(), SCHEMA_NAME_R.as_str()).to_string();
+        let err = name.map_err(|e| e.to_string()).err().unwrap();
+        assert_eq!(expected, err);
+
+        Ok(())
+    }
+
+    /// A test cases showing that names and namespaces can be constructed
+    /// entirely by underscores.
+    #[test]
+    fn test_avro_3897_funny_valid_names_and_namespaces() -> TestResult {
+        for funny_name in ["_", "_._", "__._", "_.__", "_._._"] {
+            let name = Name::new(funny_name);
+            assert!(name.is_ok());
+        }
+
+        Ok(())
+    }
 }