The shortstop was placed on the 10-day disabled list after spraining his ankle when he slipped on the dugout steps moments before the Angels took the field against Kansas City on Wednesday afternoon.
He played two innings before having to leave the game and an MRI revealed "some damage," Simmons told reporters after the Angels' 1-0 victory.
He didn't know how long he'd be out but was hopeful he'd miss no more than the required 10 games.
"I'm planning to be back on my feet, moving around, as soon as possible," Simmons said. "But got to play it smart. We'll see. I'm just (mad) I'm going to miss a couple games. That's the only thing that's really bothering me right now."
The 28-year old was batting .330 with an .860 on-base-plus-slugging percentage this season.
"He's an important guy to us," manager Mike Scioscia said Wednesday. "The way it happened is probably tougher to stomach than anything, just coming down the steps. But it happens, and we'll get back out there."
Simmons will remain in Los Angeles during the team's nine-game road swing. Utility man Kaleb Cozart was recalled from Triple-A Salt Lake to fill Simmons' place on the roster while Zack Cozart is expected to see most of the action at shortstop.
"He's an incredible shortstop," Scioscia said of Cozart. "For us to have that luxury to be able to slide him over there is something that a lot of teams wouldn't be able to do."
Albert Pujols should be back in the lineup after missing two games with a sore left knee. Combined with an off-day Thursday, he'll have had three full days of rest.
Scioscia said the injury wasn't serious.
"We're going to manage it," Scioscia said. "I don't think it's anything that we can't take care of with a little bit of rest or there. We want Albert to obviously get his looks in the batter's box. He's starting to really feel good and comfortable swinging the bat."
Right-hander Garrett Richards (4-4, 3.25 ERA) will open the series for Los Angeles. He didn't take a decision in his last outing despite holding the Rangers to an unearned run over a season-high seven innings.
Richards has been doing some good work of late, going 1-3 with a 1.89 ERA over his last six starts.
Minnesota starter Lance Lynn (4-4, 5.46) has shown improvement over his last six outings, posting a 3.34 ERA during that stretch. He limited Cleveland to a run on two hits over six innings in his last start to earn his third consecutive victory.
Lynn has been battling a nagging blister on his pitching hand for much of the season, which has had an impact on his command at times and pushed his traditionally-high fastball usage rate to 78.5 percent on the season.
"When it gets a little bit raw, it's going to affect how he's able to command and spin the ball," Twins manager Paul Molitor said. "I don't think there's been a big correlation between his command, which he struggled with early, and the fact he's starting to get better and maybe that thing is healing a little bit."
Lynn gave up four runs on eight hits to the Angles on May 11 and is 0-1 with a 7.59 ERA in two previous starts against Los Angeles.
Richards is 2-1 with a 2.97 ERA in six career outings (five starts) against the Twins, who tagged him for three runs over 5 1/3 innings in a no-decision May 10.