Coach Rob Chudzinski said the second-year pro is being held out of the three-day session "strictly as a precaution," but should be ready for the start of training camp July 26. Richardson rushed for a team-high 950 yards and scored 12 touchdowns last season.
"We don't want his muscle strain to get any worse, so we're going to rest him now and give him a full summer to prepare," Chudzinski said Tuesday after the first minicamp workout. "He could have went out, if necessary, and practiced these next few days, but we just didn't see any sense in it.
"My expectation is he'll be out there, ready to go, for us on the first day of training camp."
Richardson, the third overall draft pick in 2012 out of Alabama, sat out Cleveland's final set of organized team activities last week with the injury. At the time, he vowed, "Injury-prone is not going to be me."
The Browns did not permit Richardson to speak with the media after practice, but said he would address the subject Wednesday. The 5-foot-9, 230-pound back walked off the field without a limp and did not acknowledge the reporters following him.
Chudzinski, though, did his best to downplay the severity of Richardson's injury, which occurred in early May while running at Cleveland's team headquarters.
"I don't know the medical (risks going forward), but he's got a strain right now," the first-year coach said. "I'm not concerned about anything else at this stage.
"My only concern, really, is Trent needing to stay into it mentally while he's out. So far, he's done a great job taking mental reps and getting into game shape."
While his teammates ran position drills and 11-on-11 sets, Richardson alternated between riding the bike, lifting kettle bells and medicine balls, and working with exercise ropes.
"This is a good opportunity for other guys to get extra reps right now," Chudzinski said. "On April 1, I said this was a fresh start for everyone. I'm really pleased with the effort and energy I've seen from all of them so far."
The 6-foot, 225-pound Hardesty served as Richardson's backup in 2012, rushing for a career-high 271 yards and one touchdown. His 4.2-yard average per carry led the Browns, and was significantly higher than Richardson (3.6).
Hardesty was chosen by Cleveland in the second round of the 2010 draft, but didn't make his NFL debut until the next season after undergoing his second reconstructive knee surgery.
"Montario has done a great job in the weight room, putting muscle on," Chudzinski said. "He's got natural instincts as a runner that you can't teach. I've also been impressed with the way he's caught the ball. I don't think he's dropped one pass yet this offseason."
Ogbonnaya has been the Browns' third-down back for two seasons, catching 24 passes for 187 yards in 2012. The fifth-year pro -- also listed at 6-0 and 225 -- previously played with the Rams and Texans.
In a new twist at minicamp, Ogbonnaya saw some snaps at fullback and blocked for Hardesty on first and second downs.
"We're moving Oby around a little bit because we know he's going to do the right things," said Chudzinski, whose offensive coordinator is longtime NFL coach Norv Turner. "He's the kind of guy who is dependable and accountable, and a real asset to any team.
"Even though Trent will be back with the (first unit) when he comes back, we really like Montario and Oby, and are glad to have them as part of the group."