The Church of the Sacred Heart in Dublin Road in Cloughoge just outside Newry was vandalised overnight between Thursday and Friday.
Police were alerted to the incident at about 09:00 GMT on Friday.
Father Richard Naughton said he was distraught and that it was the first time anything like this had happened.
He said the windows would require specialist repair which would cost thousands of pounds.
“The church is a beautiful church, there are elements which make it so beautiful,” he said.
Independent councillor Gavin Malone condemned the act and said there would be a meeting next week to discuss extra security for the church.
Social Democratic and Labour Party councillor Michael Savage said it was a “despicable act”, particularly since the church had been refurbished in recent years.
“There was no justification for anybody to do this at a place of worship,” he said.
Police have asked for anyone with information or who witnessed suspicious behaviour around the time of the incident to contact them.