It happened before 11:00 a.m. Monday in Crum Lynne.
Police say a woman was walking on South Fairview Road when she was accosted by a man asking for cigarettes.
When she didn't comply, the man swung at her with a box cutter, slashing her several times in the face.
Police have released a sketch of the suspect.
He is described as a black man his late 20s, 6' 2" tall with braided, shoulder-length hair. He was wearing white T-shirt, black jogging pants and red sneakers.
Anyone who recognizes the suspect or has seen him is asked to call Ridley Township Police at 610-532-4002 or simply dial 911.