To enter Canada, the Canadian government requires a person must have received a second vaccine dose -- or one dose of the Johnson & Johnson vaccine -- at least 14 days before entry.
Houck had previously acknowledged being unvaccinated.
Players who go on the restricted list because they are unvaccinated against COVID-19 do not get paid and do not accrue major league service time.
Red Sox manager Alex Cora has missed the past four games after being infected with COVID-19. Boston infielder Jonathan Arauz has been on the COVID-19 IL since April 19.
The Red Sox recalled right-hander Tyler Danish and selected righty John Schreiber from Triple-A in corresponding moves to replace Houck and Crawford.
The Associated Press contributed to this report.