It does place an unfair burden on naturalized citizens. When possible, all citizens should shoulder the same burdens. Require proof of citizenship from all voters. For most, a simple picture ID and access to a database of citizens should be enough. For the unusual case of recently naturalized citizens who may not have such records on file, a certificate of naturalization should suffice -- but it should not be required of every naturalized citizen.
Evertyone should be proud to show that they are naturalized or native born. I DAMNED WELL WOULD BE.