The incident happened just before 10 p.m. Monday in the 1600 block of Benito Avenue.
Alhambra police say a man knocked on the door and asked for the victim by name.
He then shot her with a semi-automatic handgun and fled the scene, according to police.
Paramedics rushed her to a local hospital in critical but stable condition as police questioned several people.
Officers have not made any arrests, and a motive is unclear.