The Heat said they were "aware, but not commenting" on the incident, which ESPN reported occurred at a practice court set up in a Las Vegas hotel.
Multiple sources told The Athletic that after an exchange of words "Adebayo proceeded to approach Herro and, without hesitation, punched him."
The dispute apparently stemmed from social media comments Herro made after he was traded to the Milwaukee Bucks in the deal that sent Greek star Giannis Antetokounmpo to the Heat in June.
Herro had critiqued Adebayo's offensive abilities in comments regarding the maximum contract extension the center received from Miami.
Earlier in the day, before news of the altercation broke, Herro had spoken glowingly of his relationship with the Heat and his former teammates when he was interviewed on the Prime broadcast of a Summer League game between young squads from the Heat and Bucks.
"It's all love in Miami," Herro said. "I've seen a couple of the guys, coaching staff...we are all good in Miami."
As he departed the arena, Herro was asked about the run-in with Adebayo.
"My only comment is 'no comment,'" he said, the South Florida Sun Sentinel reported.