The incident comes following a protest held last night at the church in Berlin Street.
The protest was organised following another incident earlier in the day during which police spoke to a man “acting suspiciously” in the Paris Street area.
A PSNI spokesperson said “no offences were detected” when they spoke to the individual, but he was “given advice and guidance about his behaviour” and removed from the area.
Police are now probing the damage done to the place of worship and have urged anyone with information to contact them.
A PSNI spokesperson said: “Police received a report of a man acting suspiciously in the Paris Street area of North Belfast on Sunday afternoon, 20th July.
“Officers attended and spoke with a male. No offences were detected.“The man was given advice and guidance by police about his behaviour – and was subsequently removed from the area by officers.
“Later that evening, police received a report of a large protest at a church in the Berlin Street area.
“The protest was monitored and the crowd dispersed at approximately 8.15pm
“Graffiti has been spray painted onto the church and signs placed over windows.
“Enquiries are ongoing. Anyone with information is asked to contact police on 101, quoting reference number 1181 20/07/25.”