The Harris County Sheriff's Office said the trouble began when three robbery suspects held up a man near a barber shop just after 9 p.m. Sunday in east Harris County.
At one point, the robbery suspects opened fire on the man. Investigators say at least 10 shots were fired.
The baby was in the back seat of an SUV. When the shooting happened, the child's mother took off.
WATCH: 9-month-old baby shot in east Harris Co.
9-month-old and male shot during robbery in Harris County
Deputies said she stopped on Corpus Christi and Freeport Streets, about a half mile from where the shooting happened, before calling 911.
"The woman whose vehicle was shot, the child was inside the back seat when the shot penetrated the vehicle (when it) was parked out in the parking lot. We don't know if she was directly involved or just a bystander, we don't know that yet," said Sheriff Ed Gonzalez.
The child is said to be in stable condition. It's not clear where the baby was wounded.
The man was shot in the cheek. He was able to flee to an IHOP restaurant on the East Freeway and Uvalde before calling for help.
Houston police found the man, who was taken to the hospital in critical condition. Officers said they believe he is going to survive his injuries.
Deputies do not have a clear description of the shooter. Investigators say at least three men were involved.
The sheriff said the men should be considered armed and dangerous.