The injury doesn't appear serious, according to the Jets, but any time lost is potentially significant because Becton has battled weight and conditioning issues.
"As of now, it doesn't seem like a big deal, but -- knock on wood -- hopefully that stays the case," said coach Robert Saleh, who described the MRI as precautionary.
The 2020 first-round pick injured his right knee in the 2021 season opener and never played again even though the team initially called it a four- to six-week return from surgery.
On Monday, he labored through early offensive-line drills, checking his knee and moving gingerly. A few minutes later, on the second play of an 11-on-11 period, Becton fell backward after being jolted by defensive end John Franklin -Myers. His right foot seemed to get caught in the grass, perhaps causing his knee to bend awkwardly.
Becton removed his shoulder pads and limped immediately to the locker room with members of the training staff. He started wearing a knee brace last Friday, an indication that he may have started to feel discomfort.
The injury occurred two days after the Jets hosted free-agent tackle Duane Brown, who attended the Jets' annual Green & White scrimmage at MetLife Stadium. They remain interested in Brown, a five-time Pro Bowl selection who turns 37 on Aug. 30.
With Becton's injury, and with backup swing tackle Conor McDermott sidelined one to two weeks with a sprained ankle, there is a greater sense of urgency to add an experienced tackle. Starting left tackle George Fant also is returned from knee surgery, although he is healthy and practicing.
Saleh downplayed the team's interest in Brown, saying they have "so much great talent" at tackle and that Brown would be a luxury.
"It doesn't create panic in my mind at all," Saleh said. "A guy like Duane is a bonus."
Still, there has to be concern because of Becton's injury history. He has started only 14 out of 33 games in two seasons, including six games he didn't finish because of various injuries. His weight became a major storyline last season, when he ballooned to about 400 pounds as he recovered from surgery.
He was overweight at the June minicamp, which frustrated the organization, but he trained at the facility before training camp and reported in acceptable shape. Saleh praised Becton for powering through the first nine practices as he worked his way back into football shape.
Now it could be a challenge if he has to miss time.
"We'll see if he does take time off," Saleh said. "Obviously, you're concerned for everyone. ... You just don't want to get into a deficit of conditioning. He's a big man. He's been working his tail off and he's done everything he's been asked to do. Hopefully, he checks out good like we think he's going to and he can continue on this track. I think he's going to be fine."
Late Monday, the Jets added veteran depth by signing well-traveled veteran Caleb Benenoch, a source confirmed to ESPN. Benenoch, 28, has 23 starts in five seasons, including 22 with the Tampa Bay Buccaneers from 2016 to 2019. He spent most of last season on the New Orleans Saints practice squad, starting one game late in the year.