Wright will not be with the Heat for home games Friday against Chicago and Sunday against Philadelphia. He was charged early Thursday with DUI and driving with a suspended license after a traffic stop in Miami Beach.
"This is out of character for Dorell," Heat president Pat Riley said. "We feel he's a good person and that he will learn from this mistake."
Wright was not available for comment Friday, and has not made any public statements since the arrest. The 6-foot-8 backup forward is averaging 6.3 points in 57 games this season.
Heat guard Dwyane Wade, one of Wright's closest friends, said the team would not view the arrest and suspension as a distraction.
Miami is trying to make the playoffs and entered Friday as the No. 8 seed in the Eastern Conference, 1½ games ahead of Chicago and two games behind No. 5 Milwaukee.
"One thing about this team, everything we've went through this year, we've found a way to move on from it," Wade said. "We're a family. We understand that things happen and we all support each other. Things are unfortunate for the individual, but as a team, we all support each other and we move on."
This is the third significant off-court matter to hit the Heat in recent weeks, starting with point guard Carlos Arroyo's arrest on Feb. 26 after police in Coral Gables, Fla. said he refused to leave his vehicle after a traffic stop.
Arroyo was cited for operating a motor vehicle at such a slow speed as to block traffic, failure to obey a lawful order and resisting arrest without violence.
Last week, point guard Rafer Alston left the team without explaining why. He later told ESPN it was sparked by a crisis involving a family member, but as of Friday morning had not relayed that information to anyone within the Heat organization.
Heat coach Erik Spoelstra did not specifically discuss Wright's situation after Friday's shootaround. But he did address the cumulative effect of the three incidents.
"We represent not only ourselves but a first-class organization, something that Pat Riley and (owner) Micky Arison have spent a great deal of time putting together and building up this reputation," Spoelstra said. "So in the last three weeks, there have been some uncharacteristic moments here for the Miami Heat. But we're still a family. And people do make mistakes in the family."