Four-day-old Mychael Darthard-Dawodu was found in a home in New Mexico by police following up on tips, a day after she was hidden in the woman's purse and taken from the hospital.
"It's a joyous time," Gwen Stafford, senior vice president of Covenant Health System, said at a news conference Sunday. "This has been a roller coaster of emotions."
Rayshaun Parson, 21, was arrested on suspicion of kidnapping. Federal charges also could be pursued, Lubbock police Lt. Scott Hudgens said.
Phone numbers at Parson's address had been disconnected Sunday.
Mychael was found to be in good condition, Clovis, New Mexico police Lt. James Schoeffel said. She had earlier been reported to be suffering from jaundice, a common complication in newborns in which a buildup of pigment in the blood causes a yellowing of the skin.
The infant was kidnapped early Saturday by a woman posing as a medical worker who walked out with the 5 pound baby in her purse, police said.
Hospital surveillance footage showed a woman wearing hospital scrubs and a gray, puffy jacket with a hood walking out of the hospital.
The abductor had gone into Mychael's mother's room several times before the baby was taken, telling her the baby needed tests, Stafford said.
Newborns at Covenant are tagged with a security bracelet, said Stafford, who did not give details on how the bracelet worked.
"As soon as the baby and this security piece were separated, we were alarmed and knew," Stafford said.
"Clearly we need to take security to a higher standard," she added.
A former Covenant nurse who had a baby Friday at the same hospital told the Lubbock Avalanche-Journal newspaper that the hospital placed an electronic band on her newborn girl's ankle. She said she was told that if the baby were taken too close to a door or elevator, a sensor would cause the door to lock or the elevator to shut down.
If the band were cut off before it was deactivated, she said, the hospital would be locked down.