The accident happened at about 4:30 p.m. at Pitman Avenue and De Reimer Avenue in the Wakefield section.
Witnesses said the driver rammed into three cars, pushing one onto the sidewalk where it hit the victims, who had just come from church.
One of them, an 81-year old woman, was taken to Jacobi Medical Center in critical condition with head trauma.
The other woman, 77, is in serious but stable condition at Montefiore Medical Center.
Police say the driver is in custody, and charges are pending.
Investigators said the cars that were struck were legally parked.