The suspected robber ran up Wisconsin Avenue and the woman followed, "something I don't recommend," said MPD Lieutenant John Hedgecock.
The woman was unable to catch the suspected robber, but the phone was found in an alley off of Grace Street. The phone was returned to the victim, Hedgecock said.
Police described the suspected robber as a black male, about 5-feet-5-inches tall and wearing dark clothing.
This was the second incident in less than a week in which a phone was stolen from someone standing on a Georgetown sidewalk. On Nov. 29, a woman's phone was taken from her purse while she was feeding a parking meter.