The move was made before Tuesday's game in Detroit, where the Twins began a three-game series with the Tigers. Tonkin took the roster spot opened by the demotion of starting pitcher Kyle Gibson to Triple-A.
Tonkin appeared in one game for the Twins on July 11, recording four outs without allowing a run before being sent back to Rochester. Since then, he had six saves in 12 games with a 3.95 ERA and a .216 opponent batting average.
With Gibson out, the Twins must fill a spot in the rotation for Saturday. Manager Ron Gardenhire said after Gibson was sent down on Monday that long reliever Anthony Swarzak is a candidate.