The pastoral centre at the St Francis RC Church in Belmont was vandalised on Saturday, just as parishioners were praying.
Police have since detained the two suspects.
The two men were dressed in robes, one was dressed in yellow with a turban on his head carrying a multicoloured flag, which he used to damage the windows and destroy a statue on the compound.
He identified himself only as Ali.
The other suspect was dressed in red and white, and also had a turban on his head. He was walking around the premises at the time of the attach, chanting inaudible words. He told police his name was Anthony.
Despite the incident, there was service at the pastoral centre this morning.
The St Francis RC Church is currently in the midst of a restoration exercise.