Police say tyres were put against the Christ Foundation Counselling Ministry shop on the Donegall Road in the early hours of Sunday morning and set alight.
Some scorch damage was caused to the outside of the building.
The complex opened at the site facing Belfast City Hospital two months ago.
Pastor Oladele Abiona said the complex was used for a variety of purposes, including a counselling service, charity shop and salon.
“Ever since we started running people were coming in and they were happy and embracing the good work we were doing in the community.
“This is a place where there is no discrimination, people from every background come here.
“We’re not going to give up, we’ll continue on the good work we are doing and I believe whoever is doing this, I pray that they will have a change of mind because what we are actually doing is trying to make the community a peaceful place for everybody to be able to live in,” he said.
Detectives in south Belfast have appealed for information to contact them on the 101 non-emergency number.