Carolyn Piksa was taken into custody at her Burien home just before 5 p.m.
The shooting took place three hours earlier in the Seattle Park Department's Densmore Maintenance Facility near the intersection of North 80th Street and Densmore, about two blocks north of Green Lake.
Piksa, a Seattle Parks employee, met with some other employees at the facility, pulled out a gun and shot the 65-year-old man before leaving the scene, said Deputy Chief Nick Metz with Seattle Police.
The victim was rushed to Harborview Medical Center in critical but stable condition with a gunshot wound to the chest. He was identified as Bill Keller, the executive director of the Associated Recreation Council, a nonprofit group that works with Seattle Parks Department.
Metz said the shooter didn't target any other employee.
"I don't know if she went there with (Keller) in mind, but when she got there he was the only one she shot," he said.
Piksa then went to the Bitter Lake Community Center, at 13530 Linden Ave. N., about two miles north of the shooting scene, Metz said. There, she confronted an employee with a handgun and exchanged words but left without incident, police said.
There weren't immediate details of what she told that employee, Metz said.
The shooting prompted the city to shut down all community centers and put nearby schools on high alert. A spokesman for the Seattle Parks Department said Piksa had keys to many of the city's community centers, and all of them were placed in lockdown as a precaution.
Police used cellphone intelligence to track Piksa to her Burien home. A SWAT team arrived at the house just before 5 p.m. and set up containment, Metz said.
Using a bullhorn, officers told Piksa to come out of the house, which she did moments later, unarmed.
"She immediately came out of the house without incident," Metz said. "She was not armed and was taken to the Seattle police department's homicide unit."
Officers are searching Piksa's home, but they've yet to find a weapon, Metz said.
All parks facilities and events will be on a normal schedule Saturday, Mayor Mike McGinn said.