The incident happened on Monday in the parking lot of a Rite Aid store in the street.
Merced police say the woman had just finished shopping at the store and was walking to her vehicle when 29-year-old David Ruggiero approached her aggressively.
Police say Ruggiero tried to rip the woman's purse and car keys from her hands, but she fought back, punching him twice in the face with a closed fist before a police officer arrived at the scene.
Ruggiero was arrested and was transported to the Merced County Jail and booked for attempted robbery.
He is facing charges of shoplifting and robbery.
If you know anything about this incident, you are asked to contact Officer DeHoyos at 209-388-7816 or by email at dehoyosa@cityofmerced.org.