It happened at about 10:40 p.m. in the intersection of Wheatley and West Little York when officers reportedly heard the gunshots from a distance while investigating a nearby robbery.
Officials said the family was stopped at a red light when they heard gunfire, with no idea where it came from.
HPD said a bullet went through their vehicle and struck the mother in the legs.
She was taken to the hospital with non-life-threatening injuries, police said.
No one else was hurt.
Authorities said they don't believe this was a targeted shooting and are looking for the gunman.
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