Kubiak said Foster was on crutches Wednesday, one day after he suffered the injury on the first play of team drills during Tuesday's voluntary practice.
"He'll stay on crutches a couple of days, rehab, and we'll have him back for camp. He's going to be fine," Kubiak told reporters on Wednesday.
Kubiak said the Texans are playing things safe with Foster, who ran for 1,424 yards and 15 touchdowns last season.
"We've got two weeks left of the offseason, so [we're] obviously not going to do anything to take a risk," Kubiak said, according to the team's website. "We've got two months almost before we get ready to go. Might have ruined Arian's summer -- he's gonna have to be here a lot -- but that's OK. He's gonna be OK."
Running back Ben Tate will get the bulk of the reps during the remainder of OTAs and the team's minicamp in Foster's absence.
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.
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.
Information from The Associated Press was used in this report.