Greater Manchester Police is investigating the blaze at Heaton Park Methodist Church on Bury Old Road, at around 8pm on Saturday.
The building was severely damaged in the fire, while several computer items were also stolen.
Rev Jez Hackett told the Press Association: "Thankfully the fire seems to have been contained to just one room, the prayer room, but this is obviously a pretty nasty thing to happen, particularly at this time of year.
"We have had to cancel services at this church, although thankfully the Prestwich Methodist Church is just down the road so we will be moving services there.
"But we also run a night shelter for refugees and offer food for children on free school meals, so we don't know what is going to happen with that now."
He said insurers were due to visit the church in the coming days, but did not expect the church to re-open until at least mid-January.
Chief Inspector Jamie Collins, of GMP's Bury borough, said: "There's no way to describe the offenders' actions, other than to say they were disgusting.
"To break into a church, set a fire and then steal valuables would be bad enough any other time of the year but to do it a few days before Christmas, which is a time when many people turn to their church, is nothing short of disgusting.
"I know this incident will cause a lot of upset locally but I want to reassure the people of Bury that we are treating this as a priority and we are liaising closely with the Greater Manchester Fire and Rescue Service to establish exactly what has happened to cause the fire.
"However, we still need the public's help to find those responsible. If you believe that you can help us find them then please contact the police as a matter of urgency. We simply cannot tolerate this kind of behaviour."
Anybody with information is asked to contact police on 0161 856 8172 or the independent charity Crimestoppers, anonymously, on 0800 555 111.
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