Kawasaki was in the starting lineup Tuesday night against the New York Yankees, playing second base and batting eighth.
The 30-year-old Delabar was picked for the AL All-Star team last year and faced one batter in the showcase game, striking out Buster Posey. But the right-hander has been inconsistent this season while going 3-0 with a 4.68 ERA in 29 games.
Delabar was optioned to Triple-A Buffalo and Kawasaki was recalled from the same club. The 33-year-old Kawasaki played three games for Toronto earlier this season.