One of the children - a two-year-old - suffered life-threatening injuries.
The mother and her three-year-old were also taken to hospital and are reported to be in stable condition.
The accident happened on Bromsfrove Road, north of Winston Churchill Boulevard just before 6 p.m.
Police say the three were struck by a car while in the crosswalk.
There is no word yet on whether any charges will be laid.