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.
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 on Saturday when the 76ers visit the Portland Trail Blazers. Towns' suspension will also begin Saturday when the Wolves visit the Washington Wizards.
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.
-- ESPN contributed to this report.