MINNEAPOLIS -- Given the unusual circumstances surrounding the 2020 season, it shouldn't come as a surprise that the Twins have a rather bizarre roster situation on their hands.

Rich Hill was officially placed on the 10-day injured list on Tuesday morning with left shoulder fatigue (retroactive to Friday), and the Twins don't have a corresponding move to fill their 30-man roster. They elected to play Tuesday's game with only 29 active players and will continue to evaluate their situation in the coming days ahead of Thursday's initial round of roster cuts from 30 to 28.

"If we needed to make a move right now and we felt that was necessary or helpful to us today, we would do that, but I think we’re in a good spot health-wise with the guys that are active right now," Twins manager Rocco Baldelli said. "I think we should be plenty covered for today and tomorrow and be in good shape, but we also are leaving that spot open in case we do need something today or tomorrow."

Hill said he first felt the weakness in the back of his throwing shoulder while tossing fastballs in his start against the Cardinals last Wednesday. He was hoping to avoid an IL stint, but he said several minor issues have mounted since then that necessitate a few days for recovery. He said he has had both good days and bad days, as he was considerably sore the day after his start but felt much better the following day. But the bad days have lingered.

Hill hasn't yet thrown a bullpen session since that start but could do so either Friday, Saturday or Sunday. He said he has had some light discussions with the coaching staff with some possibilities for return dates on the Twins' upcoming road trip, though there's nothing concrete yet.

The 40-year-old left-hander had built up to 75-90 pitch bullpen sessions before he arrived at Summer Camp and his physical condition even appeared to be ahead of other pitchers due to his strict throwing regimen while awaiting baseball's restart. He threw 68 pitches over five shutout innings in his season debut against St. Louis.

"That part to me is what is frustrating about this, because of all the work that went into this and the time and leading to our Spring Training 2.0 and feeling so good coming in and throwing the ball really well," Hill said. "Obviously just need to take care of this and look forward to getting back out there."

Back to the roster situation, then: What do the Twins have to gain by playing one man down?

Even in this shortened 60-game season, players who are optioned off the active roster need to wait 10 days until they can be recalled to the Major League squad. If the Twins recalled a player to fill Hill's roster spot at this time, they would need to make a pair of cuts to trim down to 28 on Thursday, which would leave two players subject to that 10-day cooldown period before they could return to the team.

By leaving only 29 players on the active roster, Minnesota would only need to option one player on Thursday and subject him to that cooldown period.

"It puts you in a spot where if that one roster spot just also becomes one of those two that you’re going to lose in a couple of days, then it just kind of works itself out," Baldelli said.

And it’s not like the Twins need the extra body right now. Fifth outfielder LaMonte Wade Jr opened the season on the 30-man roster but only made one appearance as a defensive replacement -- at first base, to boot -- before he was optioned to St. Paul on Monday in favor of Caleb Thielbar, an extra pitcher.

Minnesota still has a full complement of 15 pitchers on its roster and is in good shape in the bullpen, as only Matt Wisler entered Tuesday having pitched on consecutive days leading into the series finale against Pittsburgh.

"We don’t know exactly in two days where we want to be,” Baldelli said, “so what we really don’t want to happen is we have to make a move today and then in two days, be forced to make another move which could put whoever we send out in a bad spot, whether they’re not available or something else is going on going forward."