Firefighters were called out to the home on Firebrick near Gateridge around midnight Saturday.
When they arrived, flames were coming from the garage and had already burned two bedrooms.
Firefighters say the mother parked her car in the garage earlier in the evening.
The car caught fire soon after and smoke began filling the house, officials said.
Firefighters from the Cy-Fair Volunteer Fire Department put out the blaze before it could do more damage.
No one was injured.