Damage was caused to the two places of worship in Newtownhamilton – St Michael’s Catholic Church on Dundalk Road and the Second Presbyterian Church on Castleblaney Street.
Police received reports of the burglaries happening sometime between 3pm on Christmas Day and 9am on Friday.
Items taken during the break-ins included electronic speakers and a wall clock.
“We are appealing to anyone that may have noted suspicious activity in the area of these places of worship...during this time frame,” a PSNI spokesperson said.
“Slieve Gullion Neighbourhood Policing Team are also aware of these incidents and have increased patrols in these areas.
“I would ask that members of the public continue to be vigilant and report to police any suspicious activity around places of worship.
”We would appeal to anyone who may have noticed any suspicious behaviour in the area.“