The small metal box in St Joseph’s Catholic Church in Meigh was damaged and had money stolen from it.
Councillor Liz Kimmins says the community has been left stunned and outraged that such an act would be carried out in a place of worship.
The box was placed next to the candles in the chapel when a thief – or thieves – went in and forced their way into it.
Councillor Kimmins said: “I share the shock and outrage of the local community at this crime and I urge anyone who might have any information that can ensure the apprehension of these burglars, to contact the PSNI”.
“People need to remain vigilant and alert to any suspicious activities. Those engaged in these criminal acts on communities, families and their properties need to face the full rigours of the law.”