Kay was placed on the 10-day injured list with a left finger blister Thursday, Mike Wilner of the Toronto Star reports.
Kay was sent to Triple-A Buffalo on Saturday, but he'll technically join the minor-league club on a rehab assignment since the injury occurred in the majors, and teams can't option injured players. It seems likely that Kay will remain with the Triple-A club once he's fully healthy, and Alek Manoah will have a chance to earn the fifth spot in Toronto's rotation after his contract was selected Thursday.