"Once he fulfills and maintains those requirements, he will rejoin the team," the Heat said in a statement, per Ira Winderman of the South Florida Sun Sentinel.
The announcement comes as a surprise based on comments Monday from head coach Erik Spoelstra, who praised Johnson's offseason work and didn't mention any potential injury or conditioning concerns.
"He's been very serious about his work this summer," Spoelstra told reporters. "You can see it in our conditioning day. He did a great job with that. He's a unique two-way player in his ability to guard 1 through 5 when he's healthy and facilitate and make other players better from a hybrid frontcourt position is unique. He's coming in healthy."
Johnson averaged 7.8 points, 3.2 rebounds and 2.5 assists across 55 appearances for Miami last season after he missed the first month of the campaign because of sports hernia surgery.
The 32-year-old Wake Forest product said Monday it's "absolutely" the best he's felt physically in a long time and he's hoping for a bounce-back season:
No further details were provided about his conditioning issues.
The Heat open the preseason next Tuesday against the San Antonio Spurs and tip off the regular season Oct. 23 when they battle the Memphis Grizzlies.
Miami's frontcourt depth is already being tested as Kelly Olynyk continues his recovery from a knee injury. Udonis Haslem should see the biggest minutes uptick in the meantime.