Kosier, also the backup center, limped off the practice field during team drills in the first of the Cowboys' two practices and walked to the locker room with head athletic trainer Jim Maurer. Coach Wade Phillips said it appears to be the same injury that's sidelined defensive lineman Marcus Spears for four to six weeks.
"It was a freak accident," Phillips said. "It could've happened at guard."
Kosier was hurt while playing center when defensive end Marcus Dixon fell on him.
"When it's not a season-ending injury it makes you feel better," Phillips said. "These guys are going to come back. We'd like to have them all right now, but we don't. That's part of what goes on. ... If it's similar to Spears, that'd be fine. If it's less than that, it'd be great."
"I feel good about Montrae," offensive line coach Hudson Houck said. "He's a good football player and he's started a lot of games in this league."
Kosier played just three games in 2008 after suffering a fracture to his right foot. But he came back strong last season and didn't miss any games. He's in the last year of his contract, which pays him a base salary of $2.9 million.
It's the second injury to a Cowboys starting offensive lineman this week. Starting right tackle Marc Colombo suffered a knee injury Monday and had surgery Tuesday in Dallas. He'll be out of action 10 to 14 days.
"We certainly like Marc Colombo and Kyle Kosier and we want them out here practicing, but it gives other guys an opportunity to step up and show that they can do," offensive coordinator Jason Garrett said. "The backup players we have here have to step up and do their jobs. ... We obviously want our starting players to be available for us, but we have backup players for a reason and we're going to give some younger guys and veteran guys a chance to come in and hopefully show they can be starters or prominent backups on our football team."
Robert Brewster, who missed all of last season with a torn pectoral muscle, will start at right tackle for Colombo.
"Looking fine," Houck said of Brewster's development. "I think he's improving. He's a young guy, a little inexperience, but he's getting better."
The Cowboys also are without backup tackle Alex Barron, who is out with a sprained ankle and won't play in a game until possibly Aug. 28 at Houston.
Owner Jerry Jones made it clear that he's not at all worried about left guard, saying, "Holland is paid what he's paid [$3.7 million base salary over two years, with the chance to make $5.2 million] in case we don't have Kosier."
But when it comes to Brewster, Jones said, "it's a horse of a different color."
"He's a rookie for all practical purposes," Jones said. "Everybody keep an eye on that right there. There will probably be some additional help in there, with extra [tight ends]."
Losing two starting offensive linemen with less than a week before the San Diego game raises serious concerns about the protection for starting quarterback Tony Romo.
"Our attitude has to be the same no matter what: Protect our quarterback, help the running game and play well," Phillips said. "I feel good about the group we have. ... I think it was smart that we have the veteran players like we have and also the young players coming up. We'll see about our depth, but I think we have a lot of depth in the offensive line."
In the second preseason game against Oakland, Romo was sacked three times on the first drive. Overall, the offensive line was credited with allowing six sacks. Romo left the game with a sore back.
"He'll play," Phillips said about Romo's status for the game versus the Chargers, adding that starters will play more than they have in either of the two games thus far. "They need to play as a team."