The Fort Bend County Sheriff's Office said the crash happened Thursday night at Bissonnet and Hodges Bend.
Authorities say they are searching for an older dark gray Nissan Altima with damage to the windshield. Deputies say the driver ran a stop sign, struck the girl and did not stop.
Lieutenant Ryan Skelton with the Fort Bend County Sheriff's Office said the girl was with her two siblings at the time of the incident.
A tweet from the sheriff's office states the girl is in critical condition after the crash.