League sources told ESPN and Newsday that Johnson sustained the injury on a long interception return after picking off a pass from quarterback Sam Darnold. He came out after the play and didn't return to practice.
Johnson is scheduled to undergo an MRI and he will be sidelined indefinitely, according to ESPN.
"Anytime a guy that makes a living running has a hamstring [injury] ... we'll see how it goes," Jets head coach Adam Gase told reporters. "He's going to have to get a lot of treatment and strengthen it up, and we'll get him back as fast as possible."
The Jets have depth issues at the cornerback position. With Johnson sidelined, the team's top three are Darryl Roberts (11 career starts), former Atlanta Falcons slot corner Brian Poole and undrafted free-agent rookie Kyron Brown from Akron.
Johnson also missed time last season due to a quadriceps injury that he suffered in practice. In his first season with the Jets in 2018, he recorded 40 combined tackles, four interceptions, one forced fumble, five pass deflections and one defensive touchdown across 10 games.
The then-St. Louis Rams selected Johnson in the third round of the 2012 NFL Draft out of Montana. He spent six seasons with the Rams before signing a five-year, $73 million contract with the Jets in the 2018 off-season.
Johnson has 368 total tackles, 22 interceptions, three forced fumbles, 72 passes defensed and four defensive touchdowns in his NFL career.