Kasem was found with his wife in Kitsap County last week, days after his daughters reported him missing from a nursing home in California.
The 82-year old suffers from a form of dementia.
Kitsap County deputies served the order, which came from a California judge.
It's unclear exactly when Kasem needs to be moved.
The move comes three days after Los Angeles Superior Court Judge Daniel S. Murphy ordered Kasem's wife, Jean, to comply with court orders allowing doctors to evaluate her husband, and also allow his daughter Kerri to see him. He also ordered Jean Kasem to surrender her husband's passport and temporarily suspended her powers to determine her husband's medical care.
Murphy's orders came after the second hearing in a week in which lawyers for Jean Kasem have said they could not disclose where Casey Kasem is located. Authorities found him in Kitsap County last week after Murphy ordered adult protective services to locate him, but the judge said the lack of additional information and cooperation troubles him.
The judge has appointed an attorney and doctor to evaluate Casey Kasem, but neither has been able to contact him or his wife.
Murphy ordered last week that Kasem, 82, could not be moved without another court order, and he stressed on Tuesday that Kasem should be medically evaluated as soon as possible.
Kasem gained fame with his radio music countdown shows, "American Top 40" and "Casey's Top 40," and he was the voice of Shaggy in the cartoon "Scooby Doo."