Rangers general manager Jon Daniels said Ogando likely won't get back on a big league mound for four to six weeks.
"It was a little more significant than we expected to see," Daniels said.
Ogando, 28, had an MRI on Monday to determine the severity of the injury. He said he felt something in his groin while beating out a bunt single in the fourth inning of Sunday's win over the San Francisco Giants.
"Right now it feels pretty bad," Ogando told reporters after the game. "I feel bad because of the situation we're in, but that's something that happens in baseball."
After enjoying a successful stint in a setup role, Ogando moved into the rotation last week when Holland was placed on the DL. Scott Feldman is winless in five starts since filling in for Feliz.
Ogando was an All-Star starter last season before fatigue forced a move to the bullpen. He was an important member of the Rangers' postseason relief corps and was a versatile part of the bullpen this season, pitching multiple innings or setting up for closer Joe Nathan.
Kirkman, 25, is 5-1 with a 5.25 ERA in 15 games (eight starts) for Triple-A Round Rock this season. Over his last seven games (five starts), Kirkman is 4-0 with a 3.38 ERA, limiting opposing batters to a .191 average with 19 walks and 33 strikeouts. He tossed a scoreless relief inning Thursday at Omaha.
Besides Kirkman, the Rangers could choose to move rookie left-hander Robbie Ross into the rotation. He pitched four innings and allowed one hit when Ogando exited of Sunday's contest.
Roy Oswalt remains on schedule to pitch Tuesday night for Double-A Frisco as he builds arm strength. It will be his third start in the minors since signing as a free agent a few weeks ago. Daniels said the right-hander will be evaluated following the start.
"Nothing has changed," Daniels said. "It's going to be predicated on how he's feeling, how he's doing and what our needs are. We want to be sure he's 100 percent ready to come up both on his arm and conditioning."
Rangers CEO Nolan Ryan told ESPN Dallas 103.3 FM's Galloway & Company on Monday that Oswalt is scheduled to start again over the weekend in Round Rock before possibly joining the rotation.
Meanwhile, there was good news on the Feliz and Holland injury fronts, according to Daniels. Feliz was examined again by doctors and is doing better. He will see Rangers physician Dr. Keith Meister again this weekend; it'll be four weeks since Feliz stopped throwing, and he could begin a throwing program shortly thereafter.
Holland has put some weight back on and is working out and should be ready to throw soon as well, Daniels said.
At this point, Daniels said going outside the organization for pitching help isn't a top priority.
"We're always going to consider all of our options and I think we're probably still a month away from the trade market really heating up, or at least a few weeks (away), but that's not where our mindset is," Daniels said. "We've gotten fairly good news on Derek and Neftali. Roy is making progress and will get stretched out. Alexi will be back. It's not a long-term injury. Our mindset is to weather the storm and get our guys back and reassess at that point."