The shooting happened around 6:30 p.m. Thursday off Scott Street near Wheeler Avenue.
Police say the mother went into a nail salon to check on wait times and it was in those moments that someone fired at least 11 shots into the car.
Authorities told ABC13 three children were inside at the time.
An 8-year-old boy was shot in the head. He's in critical condition.
The boy's 5-year-old sister was taken to the hospital with a gunshot wound to the leg.
An 11-year-old child who was also inside the vehicle was not injured.
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Police say there was an earlier shooting nearby that may be connected to this drive-by.
In the earlier incident, a 20-year-old was killed.
The violence on Scott Street is moving some in the community to demand that the shootings stop.
"People have no idea how they are breaking up families. So, we got to do something. I don't know what. The mayor and the police, we committed to bringing in 500 new officers over the next few years, we got to find money to cover that," said City Councilman Dwight Boykins.
Mayor Sylvester Turner responded to the shooting, tweeting, "I will not tolerate heinous and cowardly acts of violence against innocent children."
He added that, "We must work together to keep Houston safe."
Leaders including Rev. Marcus Cosby of Wheeler Avenue Baptist Church and Councilwoman Sheila Jackson Lee joined the mayor and Boykins in denouncing the violence, saying that the community cannot allow it to continue.
Police say it appears the car was targeted, but they still don't know who pulled the trigger.
Officials, however, did vow to find out who is responsible.
"Those who don't want to listen and just think we're going to stand by and let our streets become bloodbaths, they've got another thing coming," HPD Executive Assistant Police Chief Troy R. Finner said. "Because the majority of the people in this city are good people."
City leaders call for end to violence
WATCH: Reporter Steven Romo reports near the salon
Boy and girl shot in drive-by outside nail salon
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