Smart hoped to play in the final two classification games after the Americans were eliminated from title contention on Wednesday, but he's been experiencing soreness in his left hand and quad/calf area, prompting the decision to hold him out, according to Charania.
The 25-year-old's status was in doubt leading up to the tournament after he missed the majority of Team USA's exhibition games with a calf injury. Smart also sustained a strained left quad during the World Cup, which kept him out of the team's last first-round game against Japan.
Smart finished with 11 points, two assists, and two steals in the Americans' 89-79 quarterfinals loss to France.
During the tournament, he provided the U.S. with another ball-handler and versatile defender. He was named one of Team USA's three captains ahead of the World Cup, alongside new Celtics teammate Kemba Walker and Utah Jazz guard Donovan Mitchell.
The U.S. will take on Serbia in Thursday's classification game and can finish no higher than fifth at the World Cup.