A brick has been thrown at the front door of a church in Lurgan, breaking a pane of glass, while Remembrance Day crosses were also damaged.
Police say they are treating the criminal damage at First Lurgan Presbyterian on High Street as a hate crime.
It happened sometime between midday on Tuesday and 1pm on Wednesday.
PSNI Chief Inspector Jon Burrows said: “I would appeal to anyone with any information, or any drivers who were passing First Lurgan Presbyterian Church and who may have captured footage on dashcam that may be of assistance to our investigation, to contact officers in Lurgan on 101.
“Alternatively, information can also be provided to the independent charity Crimestoppers on 0800 555 111 which is 100% anonymous and gives people the power to speak up and stop crime.”