Rincon now has 72 hours to refuse or accept the assignment.
Once regarded as one of the top setup men in the game, Rincon, 29, has struggled to find his form over recent seasons -- most notably this year. He has posted a 6.11 ERA in 28 innings for the Twins this season, allowing 33 hits, 16 walks and five homers.
Those struggles made Rincon the pitcher to be cut since fellow relievers Boof Bonser, Brian Bass and Craig Breslow were all also out of options. The Twins placed Rincon, who is making $2.48 million this season, on waivers earlier this week, but no team was willing to take on the remainder of his salary.
"Every roster move is tough, but this one is a little tougher than most," Twins general manager Bill Smith said. "I've known Juan Rincon since we signed him as a 17-year-old in Venezuela in 1996. Our success in the early part of the decade, he was a big part of that. I have a lot of respect for who he is and what he's accomplished in his Major League career."
Gardenhire said that rather than wait until after the game Thursday, he informed the reliever about the move earlier in the day at the team's hotel.
"I wouldn't put him in that ballgame tonight," Gardenhire said. "I couldn't do that to him. So I just told [Smith], 'Let's do it now.' ... It's a hard thing to do. I tried to handle it in the best way I could rather than have him sit through the night."
By mid-afternoon, Rincon's locker inside the visiting clubhouse at Progressive Field had been cleared out and the pitcher had left the ballpark before the media was allowed inside.
Since Rincon has more than five years of big league service time, the right-hander could elect to become a free agent by refusing the assignment to Rochester. The Twins then technically would have 10 days to trade or release him. But even if Rincon chooses free agency, Minnesota would still be responsible for the rest of his salary, and another team could sign him for a prorated portion of the Major League minimum, which is currently $390,000.
Although he was not around to comment following news of the move, Rincon told MLB.com on Wednesday that if the situation came where he was offered a spot in the Minors, he would likely refuse the assignment and become a free agent.
The hope by Gardenhire and Smith is that Rincon will choose to go to Rochester and try to correct his problems there. But no matter Rincon's decision, it was a sad day in the Twins' clubhouse, seeing a longtime teammate and player gone.
"He was one of guys we trusted a lot and he got a lot of huge outs for us over the years," Gardenhire said. "More than anything else, he was just such a classy young man. He didn't duck things. If threw a bad pitch, said he threw a bad pitch. [He was] a good person and the kind of people we like to have around here.
"It's just not working out right now. He hasn't been throwing well. That doesn't mean his career is over with. Maybe a change of scenery or something like that will do him well. I wish nothing but the best for him, no matter what he decides. I hope he decides to go pitch for us in Triple-A, get some innings in and come back and help us."