Police said Phillip Leon Monroe spotted LaRelle Linton in front of the All Star Super Market, 11022 Cullen, on Saturday afternoon and opened fire.
Monroe had his 3-year-old son with him in a stolen car, officials said.
"Speaking with people out in the location, there was some type of disturbance earlier in the week between two groups of people and this may have spilled over and culminated in this shooting," said Det. Barton Nabors with HPD Homicide.
After Linton was hit, someone with him fired back, police said, and one of those bullets hit the 3-year-old.
Both the child and Linton were critically wounded. The toddler is expected to recover.
Linton is paralyzed from the waist down, doctors said.
At the time of the shooting, Monroe was already charged with murder and free on a $50,000 bond.
Monroe is accused of shooting and killing an accomplice during a robbery at a southeast Houston video store in the 8500 block of Winkler in August.
"He's dangerous. I'd classify him as a bad guy," Nabors said.
Police said a charge of aggravated assault would be added to the murder and robbery charges already pending against Monroe. He's being held without bond.
Officials are still searching for the shooter who wounded the little boy.