Foster was injured in an offseason practice on Tuesday. Tests revealed no further damage, but the strain will keep Foster on crutches for at least a couple of days.
Coach Gary Kubiak said he expects his leading rusher to be fine, but that he won't participate in the team's practices over the next two weeks.
"Don't expect me to bring him back out here," Kubiak said. "We're not going to do anything to take a risk with him ... so we'll just go to work on getting him healthy and getting him ready for training camp."
Kubiak said that Foster, who ran for 1,424 yards last season, was injured simply taking a step on a play on Tuesday. He believes Foster will be healthy in plenty of time for the start of training camp, which usually is held in late July. Kubiak expects Foster to have to be at the stadium working with the medical staff to get better for the next few weeks.
"It might have ruined Arian's summer," Kubiak said. "He's going to have to be here a lot."
Ben Tate is the only other running back on the roster that was with the team last season after Houston lost free agent Justin Forsett in free agency to the Jaguars. Houston added Deji Karim, who has just 290 yards rushing in three NFL seasons, and four undrafted rookies earlier this month to beef up the thin group.
Tate had 65 carries for 279 yards backing up Foster last season. He missed five games with injuries in 2012 after sitting out his entire rookie season in 2010 after breaking an ankle in his first preseason game. His best season came in 2011 when he ran for 942 yards and four touchdowns in 15 games.
Though Foster's injury will have Tate practicing with the first team, he wasn't that excited about the extra work he'll get in organized team activities.
"It's OTAs. I want more reps during the game," he said. "I don't really care about OTAs. It's always good to perfect your craft and get better, but it's OTAs, it's not even training camp."
Despite that, he's hoping he can contribute more this season and work with Foster to make Houston's running game better.
"I want to come in and get better every single day and do whatever coaches ask me to do to help this team take the next step," he said.
Also on Wednesday, Kubiak provided an update on injured safety Ed Reed, who had hip surgery in Colorado last month. Kubiak said he returned to his home in Atlanta this week to begin a rehabilitation program there.
Kubiak had a long talk with the nine-time Pro Bowler on Tuesday and expects him in Houston for the team's mandatory mini-camp that begins June 11.
He said Reed, who signed a three-year contract with Houston after spending 11 seasons with Baltimore, will travel with the Ravens next week as they celebrate their Super Bowl victory with a visit to the White House.