Travis hasn't played since leaving a May 16 game at Houston in the seventh inning. He was injured when he was hit by a bad hop grounder in an April 30 game at Cleveland. The injury affected his swing, causing him to bat .189 in 53 at-bats in May after batting .325 in April.
The move is retroactive to May 17.
Kawasaki is batting ninth and starting at second base against the Seattle Mariners on Friday night.
A three year veteran whose major league career began with Seattle in 2012, Kawasaki is expected to split time at second base with Steve Tolleson until the Blue Jays activate shortstop Jose Reyes (left ribs) off the disabled list, possibly as early as Monday.