The 77-year-old woman was with her husband near the junction of Marshall Street and Ackroyd Street in Morley at about 5.20pm on Friday when the robber snatched the bag from her shoulder, causing her to fall to the floor.
He ran off towards Commercial Street.
The woman had to have hospital treatment on a “significant injury” to her shoulder, police said.
Detective Constable Steve Ellis, of Leeds neighbourhood crime team, said; “This incident has clearly been a frightening experience for the victim, who was knocked to the floor with such force that she has received a number of injuries.”
Police have issued an e-fit image of the mugger, who was about 6ft tall, aged 22-26 and slim. He wore a black hooded top, dark corduroy trousers and black trainers.
Anyone with information is asked to contact Det Con Ellis via 101 or Crimestoppers, anonymously, via 0800 555111.