The NBA announced the suspension Tuesday, adding that Howard has been fined $15,000 for pushing Garnett during the altercation, which took place in the first quarter of Monday's game in Brooklyn.
Nets head coach Lionel Hollins, however, said he thought Howard took a swing at Garnett's throat. Garnett, who was ejected from the game, will serve the suspension during Wednesday's game against the Memphis Grizzlies.
"I thought he threw a punch, that is my opinion," Hollins said after Tuesday's practice. "It doesn't matter what I think. I was hoping both of the guys got thrown out because they both were in an altercation. One guy gets thrown out. They [the NBA] made that determination, and that is their job."
With 7:53 remaining in the first quarter, Garnett and Howard got tangled up as Howard was trying to catch a lob pass in the paint. After a foul was called, Garnett pushed Howard, who pushed back.
Garnett then threw the ball at Howard, got in his face and head-butted him. Garnett added a push, and Howard responded by throwing an open-handed slap that hit Garnett in the neck. The two were then separated.
Multiple players and security personnel tried to hold Garnett back, but he attempted to go after Howard again before being restrained and eventually leaving the court through the tunnel.
"It is an emotional game," Hollins said. "I am not getting into why [Garnett] did what he did. It is an emotional game, and you compete and things happen and tempers flare up a little bit and you have to pay the consequences when it is over."
ESPNNewYork.com's Mike Mazzeo contributed to this report.