The crash happened at the intersection of East Upsal Street and Chew Avenue at about 1:15 a.m.
Police said the child was not properly restrained in a car seat or seatbelt but is expected to be OK.
After the initial crash, police said the woman kept moving and hit a parked vehicle.
Both the mother and her child had to be extricated from the car.
Additional details about what caused the crash were not yet made available.