Police say the woman was arrested in Burien, a suburb south of Seattle, after they surrounded a house.
Television footage showed members of a SWAT team surrounding the house before she was taken into custody.
The woman fled from the shooting scene in north Seattle on Friday afternoon.
Wounded was 65-year-old Bill Keller. He was taken to Harborview Medical Center in critical but stable condition with a shot to the chest.
Seattle police identified the suspect as 46-year-old Carolyn Piksa, an employee of the Parks and Recreation Department.
Police initially characterized the shooting as workplace violence. The motive is being investigated.
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