A fire crew attended the blaze
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The police believe a fire at a Masonic Hall on the outskirts of Londonderry was started deliberately.
And Irish police say a blaze a short distance away, across the border at a Presbyterian church hall in Donegal, may also have been an arson attack.
They are investigating a possible link between the fires.
An off-duty fire officer discovered the blaze in the Victoria Hall at Culmore Point in Derry, at 0015 BST on Monday morning.
Scorch damage was caused to the entrance hall and stairs.
There was also smoke damage to the entire building.
The police say they are treating the fire as "malicious" and have appealed to anyone with information about the incident to contact them on 02871 367337 or on Crimestoppers 0800 555111.
In the Irish Republic, fire crews were also called to a blaze at Greenbank Presbyterian church hall at Quigley's Point early on Monday.
The hall was destroyed in the fire and police say that it may have been started deliberately.
The caretaker of Greenbank church, Charlie McCauley, said the whole community was outraged by what had happened.
"I am shaking, thinking about it. It is absolutely unbelieveable. I just can't believe this would happen deliberately, not in this area," Mr McCauley said.
"I am a Catholic myself and most of my workers are Catholics. I am absolutely disgusted... I would bet my life that it is nobody involved from this area."