Robertson has won only once in his past 11 starts, is 7-10 with a 6.09 ERA and opponents are hitting .318 off him in 26 starts. He has permitted 25 home runs, tied for the most in the American League.
"He was going out there without his slider," Tigers manager Jim Leyland said. "That's his big weapon and he doesn't have it. So, he is in the bullpen."
Robertson has made only two relief appearances in 162 games with the Tigers. He has made 120 starts since his previous bullpen appearance on April 10, 2004, at Minnesota. The Tigers signed Robertson, who turns 31 on Sept. 3, to a three-year contract extension for $21.25 million in January.
"Skips got a job to do and has to make the best decision for the team," Robertson said. "He can't feel good about putting me out there with what happened in Texas. I don't feel good about going out with what happened in Texas."
Leyland said he is uncertain who would replace Robertson in the rotation. His next scheduled start would have been Tuesday against Cleveland.
It appears doubtful left-hander Dontrelle Willis, who is 3-1 with a 4.28 ERA in five starts for Triple-A Toledo, will start in Robertson's place.
"As we speak today, the answer is 100 percent no," Leyland said. "It's not the right thing to do and [general manager] Dave [Dombrowski] agrees with it."
Willis, who was acquired in a blockbuster eight-player trade last December with the Florida Marlins, was 0-1 with a 10.32 ERA in five games, including four starts, earlier in the season with Detroit. He walked 21 in 11 1/3 innings.