In a press release Saturday, Harris County Sheriff's Office investigators identified 20-year-old Eric Black Jr.as an alleged culprit in the December 30 attack.
A tip from the public helped police identify Black, who is now in custody in East Harris County.
Based on a description from one of the occupants of the Barnes family auto, authorities had been searching for a white man, raising concerns the shooting was racially motivated.
The Harris County Sheriff's Office in Houston, which is leading the investigation, said it's already working with the FBI and other federal agencies.
Currently, investigators do not think that the family was targeted intentionally, suggesting it was a possible case of "mistaken identity".
Some activists and the family, who are black, believed the unprovoked nature of the crime in a part of Harris county known for racial tensions pointed to the possibility of a racially motivated attack. Jazemine was not responding after being shot in the head.
After the shooting, one of Jazmine's siblings discovered that Jazmine had been hit.
The sheriff's office said in a release that investigators are pursuing evidence that could lead to additional people being charged in the case.
Saturday, hundreds attended a rally outside the Walmart near the road where Jazmine was killed. Prosecutors say he was driving the vehicle that pulled alongside the Barnes family auto and that someone else shot into the auto.
The shooting took place at a stoplight while Jazmine, her mother and three sisters were on their way to the grocery store.
The Sheldon Independent School District said in a statement that Jazmine was a second-grader at Monahan Elementary in Houston. The victim was black and the suspect is described as a white man in his 30s or 40s, who was wearing a hooded top and driving a red truck. They've worked on several cases together over the years, including the killing of Antwon Rose II, a black teenager killed by police outside Pittsburgh in June.
"I just want anybody, whoever, out there that knows anything about the murder of my daughter, to just please step up as if it was your own", he said. S. Lee Merritt, an attorney advising Jazmine's family, also joined the cause.
Black said he thought it was a vehicle he had seen the night before, he didn't realize who was inside.
More than 2,700 people have donated to a GoFundMe set up for Jazmine's funeral expenses and family. Her funeral is on Tuesday.