The 11-year major-league veteran, who is 10th on the league's career saves list with 324, left after a painful performance Sunday in a simulated game.
His locker was cleaned out and the nameplate removed, and he could not be reached for comment on Monday.
The four-time All-Star struggled mightily in his inning of relief at Joker Marchant Stadium, which included a long home run to nonroster invitee Mike Rabelo.
"Obviously, in his mind, he doesn't think that he's ready to compete at this level," Tigers manager Jim Leyland said Monday.
Percival partially tore a muscle near his pitching elbow last July and hasn't been the same since.
After signing a two-year, $12-million contract before last season to be the Tigers' closer, the injury limited Percival to 26 appearances.
The 36-year-old was a disappointing 1-3 with a 5.76 ERA and eight saves last season.
Percival spent the first 10 years of his career with the Los Angeles Angels, which included a string of seven consecutive 30-save seasons, and helped the Angels to the World Series championship in 2002.
He has told reporters that he's in pain when he pitches and had to change the mechanics of the way he throws.
"I went seven months without picking up a baseball and I'm still struggling out there right now," he said before Sunday's outing.
The Tigers were prepared not to have him for the 2006 season.
"Never was I counting on him or not counting on him," Leyland said. "The plan was to get him in here and we'll see what unfolds and we'll take it from there."
"We've got a lot of equipment out there," Leyland said of his bullpen. "We'll just have to see how it works out."
Still, Percival will be missed.
"Any major-league manager would like to manage a guy like that," said Leyland.