Irving (knee), Smart (thumb), Jaylen Brown (concussion), Daniel Theis (knee), Gordon Hayward (ankle) and Al Horford (illness) are all out for Boston. The Celtics also listed Jayson Tatum as probable with lower back tightness.
Irving is expected to take an extended rest due to lingering tendinitis in his left knee that forced him to sit out the second half of Sunday's loss to the Indiana Pacers. Smart sprained his right thumb in the same game while diving to the floor, and the team is getting more information on the severity of his injury while determining whether he'll be able to return to action this season.
Theis tore his meniscus in the final minute of Sunday's game and is expected to miss the remainder of the season. Brown is still in the early stages of the NBA's return-to-action concussion protocol and is not expected to play this week. Hayward is not expected back this season while rehabbing from a fractured ankle.
Horford missed Sunday's game due to illness and did not practice Monday. The Celtics did not practice Tuesday due to blizzard conditions in the Boston area.
Tatum, if he plays, and Aron Baynes would be Boston's only typical starters available. Terry Rozier seems likely to elevate to a starting role, while Marcus Morris started in place of Horford on Sunday.
"[A rash of injury] sucks but it's part of the NBA. It happens," said Rozier. "A lot of teams are going through that. Collectively, as a group, we've just got to do what we can to pick up guys, and it's not going to be easy but part of the NBA, this is what it's about, opportunity."
Added Morris: "It's the NBA. Lot of injuries, lot of wear and tear on guys' bodies. It's why you've got  players on the roster."
The Celtics were expected to recall rookie Guerschon Yabusele from the G-League to add available depth. Yabusele hasn't played in an NBA game since early February.
"We are equipped and we will battle on, I think is the way you gotta look at it," Stevens said. "I've never been in a season that's been like this. Obviously it started right out of the gate this way with Gordon. But, the rest of the year, we've dealt with what would be small, week-to-week or couple-weeks-out type things."
Despite the injuries, the Celtics (46-21) are seemingly entrenched as the No. 2 seed in the East. Two head-to-head matchups remain with the East-leading Raptors, but Toronto owns a 3.5-game lead entering Tuesday's action. Boston has a seven-game lead over the surging Indiana Pacers, the closest rival behind the Celtics.