Two masked men used an angle-grinder to cut a hole in the shutters of the Universal Church of the Kingdom of God in Templemore Street shortly before 21:30 BST on Tuesday.
A flammable substance was thrown inside and set alight.
Firefighters put out the blaze, which damaged the shutters and the building's front hall.
More smoke damage was also caused inside.
Democratic Unionist Party leader and Belfast East MP Gavin Robinson said the attack was "deeply dispiriting".
"My colleagues and I believe in our community that we are better than this and it should not be happening," he said.
"I want to encourage those within the community, not only commend them last night for contacting police and the fire service, but to encourage them further still to give information to the police to make sure that those who are responsible for this attack are apprehended."
Mr Robinson and Ulster Unionist assembly member Andy Allen visited the church in east Belfast.
Alliance Party assembly member Peter McReynolds also condemned the attack, which he said was completely unacceptable and truly appalling.
"There is no place in our community for such hatred and discrimination," he said.
"I am thankful that there have been no reported injuries from this dangerous attack, and my thoughts are with the members of the church who are now left to pick up the pieces."
The Universal Church of the Kingdom of God said ''it is regrettable that anyone would think of and cause damage to a Christian church that works extremely hard to help and support the local community.
''We do not know what the reason for the attempted break in is, and won’t speculate, but there is no good reason for causing damage to a property.
''The Help Centre remains open as usual, and the Pastor and volunteers are ready to support the community with our daily schedule of prayer services and one-to-one advice sessions.''
'Deeply saddened'
East Belfast Churches Network also condemned the attack on the building, which it says provided a help centre.
"Racism has no place in our community," it said in a statement.
"We are deeply saddened that this has happened, especially to a church and organisation which seeks to help people regardless of race or creed here in east Belfast."
The church, which has been in east Belfast since 2012, is part of a network that operates in more than 100 countries, with 40 churches across the UK.
It was formed in Brazil in 1977.