A WOMAN shot and killed a mother before abducting her newborn baby outside a health clinic in Texas.

Kayla Marie Golden, 28, had taken her three-day-old son for a checkup at a pediatrician's office in The Woodlands, 51km north of Houston, when she was shot outside the clinic, the Houston Chronicle reported.

Authorities said Golden was seen arguing with another woman who then pulled out a pistol and shot her several times.

The healthy infant was found about six hours after the shooting, Montgomery County District Attorney Brett Ligon said.

Ligon wouldn't say where the infant was found, but he said the baby was being reunited with his father.

A person of interest has been detained, though no charges have been filed, Ligon said.

The woman took the three-day-old - identified by media as both Keegan Golden and Keegan Schuchardt - who was strapped into his infant carrier and fled with a man who was driving a light blue or sea-green newer model four-door Lexus, myFOXhouston.com reported.

The injured Golden attempted to stop the car, but she was struck by the vehicle as it fled and knocked to the ground, the Chronicle reported. Golden was later pronounced dead at Hermann Memorial Hospital.

An Amber Alert was issued for Keegan, who is described as being 22 inches (56cm) and six pounds (2.7kg) with short brown hair. He was wearing a green and white onesie with "Handsome" on the front, myFOXhouston.com reported.

His kidnapper is described as a black woman who was wearing a gray sweatshirt and blue jeans.