The woman, seen in surveillance video, went to the salon in the 12100 block of Ventura Boulevard for a manicure and pedicure on June 20.
While getting the treatments, she spotted a wedding ring belonging to another woman on a side tray.
She took the ring and put it in her purse, police say.
She finished her treatment, paid for the service and left with the ring.
Anyone with information is asked to call LAPD Det. Joseph Hampton at (818)754-8377 or provide anonymous information to Crime Stoppers at (800)222-8477.