Assistant coach Greg Buckner will serve as head coach vs. the Bulls.
The Cavs said Bickerstaff is expected to return for Friday's game at Charlotte.
"It's a conversation about approach and a maturity level that we've yet to reach," Bickerstaff said of the loss. "The thought that we wouldn't come out tonight and play spirited basketball is disappointing."
He added: "I love the dudes in that locker room. I think their hearts and minds are in the right place. But we've got to grow up. It's that simple."
Larry Nance Jr. missed Monday's game for personal reasons.