The incident happened at the one-story Arverne Pilgrim Church and Arverne by the Bay Community Center on Beach Channel Drive in the Rockaways just before 3 a.m.
The driver was treated for a non-life threatening injury.
The crash caused a gas leak, and buildings department inspectors were checking the structural integrity of the building.
The church still hasn't completed repairs following Superstorm Sandy.
"We are now recovering from Sandy, and we are in the process, we had to gut the whole place to get the mildew out," Pastor Dennis Loncke said. "So now we are in the process of putting up the walls, and the windows installed. So all the things that we had in there, women's bathrooms, is crushed and stuff like that."
Officials say about 90 percent of the sheet rock work inside the building had been completed and all the mold removed. At one point after the storm, there were 54 inches of water inside.
The cause of the crash is under investigation.