An off-duty Harris County Sheriff's Office deputy working an extra job at Saks reported the incident, which happened on Oct. 24.
According to officials, the woman was apparently followed as she left a Bank of America in the 5100 block of San Felipe after withdrawing cash.
She parked in the Galleria's purple garage and rode the escalator from the garage up to Saks.
Officials say a woman in front of the victim on the escalator asked her a question, distracting her. That's when a man grabbed the victim's Chanel purse and cut it off.
The victim's family says she was injured, suffering scratches and bruises.
Saks Fifth Avenue has said it is not commenting on the ongoing investigation at this time.
Woman on hunt for purse snatchers gets threatening calls
Thief runs across road with woman's purse and gun
Purse theft victim dies after she was run over by robbery suspects
Thieves cut through walls to steal $150K in designer handbags