Baker, who allowed five runs on nine hits over six innings in the Twins' 8-6 loss to the Red Sox on Monday, missed 14 games in mid-July after being placed on the disabled list with a right flexor muscle strain on July 7.
He said after Monday's start that his elbow "feels average," and he met with team doctors on Tuesday before deciding it would be best to be placed on the 15-day disabled list even though he did not undergo an MRI.
"We'll just let everything calm down in his arm," manager Ron Gardenhire said. "It's the same thing he's had. He has a little tendinitis in a muscle near his elbow. It's just not going away, so they're going to shut him down. So no throwing until we get back from the road trip [on Aug. 18], and then we'll see where we go from there."
Baker, who had a 3.01 ERA in 17 starts before his injury, had a 4.29 ERA over his last four outings after being activated from the disabled list on July 23. But he's been the club's most consistent starter this year, with a 3.21 ERA and 120 strikeouts and 32 walks in 131 2/3 innings.
Gardenhire said he hoped Baker won't be shut down for the rest of the season, but it's still a possibility, especially considering the club is 10 1/2 games back entering Tuesday night's game against the Red Sox.
"We'll just have to let [the doctors] determine that," Gardenhire said. "We just can't let it continue like it is. He's feeling it."
Slowey, meanwhile, posted a 3.60 ERA with 38 strikeouts and six walks in seven starts totaling 50 innings with Triple-A Rochester.
He originally made five starts with Rochester as part of a rehab assignment because of a strained abdominal muscle that landed him on the disabled list on May 21. He was activated from the disabled list on July 21, but remained in the Minors because the club didn't have an open spot in its rotation.
Slowey began the season in the Twins' bullpen, but had trouble staying healthy in his new role, as he was also placed on the disabled list on April 9 with right shoulder bursitis and didn't return until June 17.
He has a 4.91 ERA in six relief appearances with the Twins this year, with seven strikeouts and one walk over 14 2/3 innings.
Right-hander Anthony Swarzak, who has a 3.20 ERA in 59 innings with Minnesota this year, was also considered as a possibility to join the rotation, but Gardenhire opted to keep him as the club's long man despite his success in five spot starts with a 3.16 ERA.
"It didn't make sense, honestly, especially with a good pitcher like Slowey down there throwing the ball good," Gardenhire said. "He's doing well, and he's healthy. We don't have enough pitching in place to really take him out. Slowey can't come up here and go out of the 'pen. So this is the right thing."
Slowey was also a candidate to be moved before the July 31 Trade Deadline, and could still be dealt before Aug. 31. But it's a complicated process, as deals involving players on the 40-man roster cannot be made unless the players already have cleared waivers.
In other words, the player must be offered to the other teams in reverse order of the standings, and if he is claimed by one of the teams, he cannot be traded to a team other than the club that claimed him. The club that placed the player on waivers can either withdraw the request and keep the player, work out a trade or let the player go to the claiming team, which would then have the rights to the player.