Officers in Newry said the incident at First Presbyterian Church (Non-Subscribing) on Wednesday evening was a "callus" and "targeted" attack.
In a statement, the Police Service in Northern Ireland said: "Some senseless person caused significant damage to a window of the church in a targeted attack.
"For any place of worship to be attacked is not just an insult to the whole community of Newry but a deplorable hate crime that has no place in our society."
Work to repair the window after previous damage was only completed a fortnight ago. Rev Norman Hutton from the church told the BBC the incident was "extremely upsetting".
Mr Hutton also told the broadcaster: "The church has undergone, over the last three or four years, a complete refurbishment on the outside and it's in prestige condition at this present time.
"But it's very upsetting for the people in the area who were delighted to see the church put back to its former glory."
Anyone with information is being asked to call 101 and quote the reference number 408 of 28/03/19.
Alternatively, they can call Crimestoppers with any information anonymously on 0800 555 111.
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