The man forced his way into this northwestern US city's Jewish Federation on Friday after an employee had punched in her security code, said Marla Meislin-Dietrich, a colleague who was not in the building at the time.
Staff members said the man said "I am a Muslim American, angry at Israel" before opening fire on everyone, Meislin-Dietrich said.
"He was randomly shooting at everyone," she said.
Police would not confirm the account of what happened.
Soon after the shooting the police arrested a man, Naveed Afzal Haq, for suspected murder and attempted murder.
When asked if the suspect was a Muslim, the police chief, Gil Kerlikowske, said at a news conference: "You could infer that that was his background."
Laura Laughlin, special agent in charge of the Seattle FBI office, said the suspect is a US citizen who is not from Seattle.
Haq, 30, previously lived in Pasco in southeast Washington state, police said in a statement.
Haq had a lewd conduct charge pending against him in Benton County, near Pasco, where he was accused of exposing himself in a public place, his attorney, Larry Stephenson, told The Seattle Times.
Stephenson said he did not believe Haq had a job.
The five wounded women were taken to Harborview Medical Centre, three of them in critical condition, a hospital spokeswoman, Pamela Steele, said.
Deanna Nollette, a police spokeswoman, said the person shot dead was a woman.
The names of the victims were not immediately released.
Greg Nickels, the mayor, and Kerlikowske said officers were moving to protect synagogues and mosques around the city, but said there was no evidence of a broad threat.
"This was a purposeful, hateful act, as far as we know by an individual acting on his own," Nickels said.
Kerlikowske said officers were protecting mosques "because there's always the concern of retaliatory crime".
The authorities have been advising synagogues and Jewish groups to be watchful in the weeks since hostilities erupted between Israel and Lebanon.
The Jewish Federation's website describes its mission as "to ensure Jewish survival and enhance the quality of Jewish life by meeting needs locally, in Israel and worldwide".
It was among the sponsors of a Solidarity With Israel rally last weekend.