It happened around 11:20 Saturday night on the 2100 block of North Marvine Street.
Arriving officers heard several shots ring out and reported seeing four men running from the scene.
The female victim - in her 40s - suffered a gunshot wound to the side and back. She was taken to Temple University Hospital in critical condition.
Officers stopped several people and have taken them in for questioning but no arrests have been made.
The latest incident is at the same apartment complex where a 10-year-old boy was shot while trying to protect his younger brother from gunfire.