The suspensions, announced Thursday by league vice president Kiki VanDeWeghe, also noted the players' "continued escalation following the incident."
Embiid and Towns became tangled in the third quarter of the Sixers' 117-95 victory and wrestled each other to the floor before coaches and teammates separated them. Towns initially threw a punch that didn't land on Embiid, who later poked Towns in the eye with his thumb. The two were ejected after a video review.
The 76ers' Ben Simmons was not disciplined for his role in the skirmish.
At the bottom of the scrum, Simmons at one point had his forearm around Towns' throat as he forcefully held his opponent down. The officials deemed Simmons a "peacemaker" who was trying to break up the fight. The Timberwolves disputed that characterization, league sources told ESPN's Adrian Wojnarowski.
Embiid reveled in the skirmish on his way off the court, shadow boxing and pumping his arms to the frenzied Sixers fans before disappearing into the tunnel.
Embiid and Towns also exchanged barbs on social media late into the night, including some coarse language.
Embiid will begin serving his suspension Saturday, when the 76ers visit the Portland Trail Blazers. He's averaging 23.3 points and 10.3 rebounds in three games this season.
Towns' suspension will also begin Saturday, when the Wolves visit the Washington Wizards. He's averaging 27.3 points and 11.5 rebounds in four games.
Timberwolves president of basketball operations Gersson Rosas issued a statement saying, "While we are disappointed with the league's decision, we understand the magnitude of this unfortunate incident. The NBA is highly competitive, and last night was a reflection of that. We support Karl and will move forward together as a group."
ESPN's Adrian Wojnarowski contributed to this report.