The pair were hit as they crossed Lichfield Road, in the Aston area of Birmingham this morning at 10.50am.
Officers said that the woman was taken to hospital with serious injuries.
The child was not hurt.
The driver stopped at the scene.
Detective Sergeant Paul Hughes from the Serious Collision Investigation Unit, said: “We’re currently in the process of piecing together what happened leading up to the collision.
“We’re collating and reviewing CCTV footage, speaking to the driver and taking statements from witnesses.
“It happened near to the railway bridge.
“I would urge anyone who saw anything to get in touch as soon as possible.”
Lichfield Road remains closed in both directions.
West Midlands Police added: “Enquiries continue and anyone with information is urged to contact us via Live Chat at west-midlands.police.uk between 8am – midnight, or call 101 anytime.
“Please quote log number 870 of 6/12/18.”