The Houston Police Department said the wreck happened at North Shepherd at Tidwell, where traffic lights weren't functioning.
Investigators said the intersection was being controlled by stop signs in the meantime.
A driver allegedly ran one of the stop signs and crashed into another vehicle, according to police.
One car had four passengers, including two children, and the other vehicle had a single driver.
A baby and both drivers were taken to the hospital.
Lt. Larry Crowson said the baby is in critical condition. It is unclear which driver ran the stop sign, and an investigation is underway.