Smoak has a left quad strain, and Jackson has a lower back strain. In corresponding moves, the Blue Jays recalled outfielder Billy McKinney and pitcher Justin Shafer from Triple-A Buffalo.
Smoak last played Friday, missing Tornoto's past three games. The 2017 All-Star is hitting .225 with 12 home runs and 34 RBIs in 62 games this season. Smoak has 75 home runs since 2017.
Jackson joined the Blue Jays as a free agent in May. Toronto is the major league-record 14th team for which he has pitched. The 35-year-old has a 12.43 ERA in seven games this season, including five starts.