The move is retroactive to June 27.
To take his place on the roster, the Tigers purchased the contract of left-hander Fu-Te Ni from Triple-A Toledo. He was 3-0 with a 2.60 ERA there, with 32 strikeouts in 24 appearances.
Robertson is 1-0 with a 7.71 ERA with the Tigers this season.
Figaro (1-1) gave up 10 hits and eight runs in six innings in Saturday's 8-1 loss in Houston, his second major league start.
The 23-year-old French will start Friday's game in Minnesota. French is 4-4 with a 2.98 ERA in 13 starts for Toledo this season.