The woman shot Golden up to seven times and snatched the baby from her arms before driving away.
Prosecutors suspect the attack may have been part of a plan to abduct any baby.
Brett Ligon, a district attorney, told ABC's Good Morning America programme that Verna McClain, 30, had been charged early on Wednesday in the killing.
According to ABC News, Ms McClain is a registered nurse and mother of three.
Mr Ligon told ABC: "There were statements as indicated in the arrest record that were made by Ms McClain that led us to believe that, in fact, this was an intentional act on her part.
"Not that Ms Golden was targeted specifically, but that this was part of a plan to kidnap a child."
The stolen baby was found unharmed on Tuesday evening and has been reunited with his family, a Child Protection Services spokeswoman told the Houston Chronicle newspaper.
It is not known where authorities found the infant, but they said the baby was not in a home raided by armed police on Tuesday evening.
Golden had taken her son to Northwoods Pediatric Center in the town of Spring for a routine check-up earlier that day.
Witnesses say there was an argument between Golden and another woman outside the building, before the attacker opened fire. A receptionist at the paediatric centre said that Verna McClain was not an employee there.
The dying woman leaned into the vehicle and tried to take her child back, screaming "my baby!" but her attacker sped away.
Reports suggest there was a second person in the car.
Linda Golden, the victim's mother, told the Associated Press news agency: "I wanted to kiss her before they put her in the ambulance."
"That's the hardest she's ever fought," Ms Golden added. "She died trying to save her baby."
Speaking to Houston television station KHOU on Tuesday, Keegan's father, Keith Schuchardt, paid tribute to Golden.
"She was sweet, lovable," he said. "I loved her and she loved me."
Days earlier, Mr Schuchardt had announced the birth of his son on Facebook: "Baby Keegan is here, born 4/14/12, 6lbs 15oz, 20 inches long. Looks like me lol."