Chalmers will serve his suspension for Saturday's game against the Charlotte Bobcats.
Heat coach Erik Spoelstra said he disagrees with the NBA's decision.
"It is disappointing about the suspension and we disagree with the suspension," Spoelstra said before the Bobcats game.
"Mario doesn't have a reputation as that type of player. ... We don't have to agree with it. What we can do is agree to disagree."
Chalmers hit Nowitzki with a forearm to the head and neck area as he came off a screen in the fourth quarter of the Heat's 110-104 victory Friday. Officials called it a flagrant foul 2 and ejected Chalmers from the game after a video review.
Officials called a normal foul on that play, but after review, the NBA upgraded it to a flagrant foul 2 and fined him $15,000.
Chalmers told reporters on Friday that he hit Nowitzki as he was trying to pull his arm away from Mavericks center Sam Dalembert, and it was an accident. Chalmers was engaged with Dalembert just before the play and quickly helped Nowitzki up from the floor.
"Dalembert had my arm so I had to get my arm free," Chalmers said. "There was nothing intentional about it. I didn't even see Dirk."
Spoelstra was just as concerned about the ramifications of any future flagrant foul on Chalmers.
"Mario is going to have to be very smart about it from here on out," Spoelstra said.
Chalmers has four suspension points by the NBA standards. That means he could face further suspensions with two more regular flagrant fouls or one more flagrant foul 2 call.
"The penalty seems very severe," Spoelstra said.
The suspension will cost Chalmers approximately $36,000 in salary. He has said he's already appealing his previous $15,000 fine.
Norris Cole will start for the Heat against the Bobcats.
Chalmers posted on Twitter Saturday:
My teammates gonna hold it down for me tonight against the bobcats. Can't wait till Tuesday night. It's startin to get personal now
— Mario Chalmers (@mchalmers15) November 16, 2013
The Heat play at home Tuesday night against the Atlanta Hawks.
Information from The Associated Press was used in this report.