West Yorkshire Police said officers were called to Regent Street in Leeds at around 11.58am on Sunday after a silver Peugeot left the road and crashed into the building, reported to be a Universal Church of the Kingdom of God Help Centre.
A 26-year-old female passenger in the vehicle has been taken to hospital in a critical condition, while the driver and other passengers - including two adults and a baby - suffered minor injuries, the force said.
A spokesman said a blue Audi had been involved in the collision and that the driver of that car, a 27-year-old man, has been arrested on suspicion of driving whilst over the prescribed limit.
Two children who were on the pavement when the crash happened suffered minor injuries, the force said.
A spokesman added: "The road is still closed, and could be for some time whilst police carry out their investigation.
"Officers are appealing to the public for witnesses to the collision itself or if anyone saw the vehicles prior to the collision."
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