The incident occurred on Eliza Street, off Albert Street, around 11am.
The driver of the car, an elderly male, was treated by paramedics at the scene.
His injuries are not thought to be serious.
Engineers have been called out to assess the structural integrity of the building.
Eliza Street is a small street accessible only from Albert Street.
The car was driven straight into the block. It is not known if it had been heading down Dura Street and cross the pavement separating it from Eliza Street or if the driver had been trying to make a turn and lost control of his car.
Man treated at scene after car smashes into Dundee tenement
