Washington, the hardest hit state in the outbreak of COVID-19, has confirmed 538 cases, Inslee said at an afternoon press conference at the statehouse in Olympia.
The U.S. coronavirus death toll reached 46 on Friday.
Inslee, a 69-year-old Democrat, said he had issued new executive orders closing all public and private K-12 schools from Tuesday through at least April 24 and extending a ban on gatherings of 250 people or more statewide.
"I don't take these decisions lightly, I'm doing this for the health of all Washingtonians," the governor said.
The bulk of the deaths from coronavirus in Washington state centered on a long-term care facility in the Seattle suburb of Kirkland.
President Donald Trump declared a national emergency over the fast-spreading virus on Friday, allowing more federal aid to combat a disease that has infected over 138,000 people worldwide and left more than 5,000 dead.