Bulls executive vice president John Paxson, who announced the ban, also said Mirotic, of Spanish and Montenegro citizenship, will miss four to six weeks after suffering upper jaw fractures and a concussion in Tuesday's altercation.
"Both players owned responsibility in the incident itself but only one player threw a punch," Paxson said. "And that punch connected. For us, that is inexcusable. It's not who we are. It disappoints us."
Mirotic's concussion symptoms must subside before his facial injuries can be addressed, Paxson said.
Portis begins serving the ban Thursday when the Bulls play their season opener at Toronto. While unable to play, Portis will be able to continue practicing with the team.
"Bobby Portis is not a bad person," Paxson said. "He's a good kid. He's a competitive kid. But in this instance, he made a mistake. And as we all know when you make mistakes, you have to suffer the consequences."
Mirotic fell to the floor after being struck and stayed there several minutes before rising. He was taken to the hospital and discharged Tuesday.
Mirotic, 26, averaged 10.6 points and 5.5 rebounds in 70 games last season and was expected to have a starting role for the Bulls this season after inking a two-year deal worth $12.5 million with Chicago.
Portis, 22, averaged 6.8 points and 4.6 rebounds in 64 games last season and was competing with Mirotic to start at power forward. He averaged 6.9 points and 5.0 rebounds over 126 games in the past two seasons after being taken by Chicago in the first round of the 2015 NBA Draft.