Jacque Vaughn, coaching the team following the ousting of Steve Nash, said on Thursday after practice that Simmons has been getting treatment in hopes of reducing the swelling.
Vaughn said Simmons wouldn't play at Washington on Friday nor at Charlotte on Saturday, although he didn't rule out Simmons being ready on Monday at Dallas in the final game of the trip.
Simmons, the No.1 pick in the 2016 draft, is returning to action after missing all of last season.
He didn't play to begin the year in Philadelphia because of mental health concerns, then injured his back after being traded to Brooklyn in February in the deal headlined by James Harden.
Simmons eventually had surgery to repair a herniated disc.
He averaged 6.2 points in Brooklyn's first six games before missing the last two.