The specifics of that conduct remain a mystery. Green was briefly hospitalized last week for still-undisclosed reasons and has not been with the team since.
He was a key reserve in Miami's first three games, missed the game Nov. 3 because of what the team said was an illness and then needed to be transported by ambulance to Jackson Memorial Hospital the following morning.
"I want to apologize to my family, fans and the Heat organization," Green said in a statement released by the team. "I accept the suspension and look forward to rejoining my teammates this weekend."
The first game of his suspension was Tuesday's 101-88 victory over the Los Angeles Lakers. He will also miss Thursday's game against Utah, so the next game he will be eligible to play is Nov. 17 against Minnesota.
"We'll work him back," Heat coach Erik Spoelstra said. "I don't think it'll take long. He was playing great basketball before that. We have practices this weekend. He'll be able to get into a flow and a rhythm, and we'll go from there."
Spoelstra said he had no concerns about Green's being able to fit back into the team dynamic, a sentiment echoed by Heat president Pat Riley.
"He's really a great kid," Riley said. "He's a great athlete, can really shoot the ball. He's explosive. We're going to need him, and I believe that he's going to show that to us."
Police said they assisted fire rescue personnel with Green's transport from a Miami apartment building, but no charges were filed and no incident reports were released publicly. The Heat were in regular contact with Green throughout his absence but have offered no details on why he was hospitalized or where he has been since, citing privacy rules.
Green has averaged 10.3 points in his three appearances with Miami, with whom he signed as a free agent in July. The two-game suspension will cost Green roughly $25,000 in missed salary.