The attack happened about 1:50 p.m. in the 22900 block of 76th Avenue W, Edmonds police Sgt. Mark Marsh said.
The woman, 29, of Edmonds, was near her car. She was punched in the face. The man took her purse and ran away.
Edmonds, Lynnwood and Mountlake Terrace police joined in the search, including police dogs.
Police believe two men were involved in the robbery. One, 39, of Lynnwood, was arrested Tuesday.
The second man was described as white, about 30, and 5-foot-8 with a thin build. He had a beard and was wearing thick clear glasses, a white undershirt, black pants and a white baseball hat with a red brim.
Anyone with information should call 425-771-0212.
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