The 6-foot-8, 250-pound Smith, who suffered the injury during Monday's practice, missed the Crimson's first 17 games with an injury to the same foot. He returned to play two minutes in an 80-50 win against Dartmouth.
Though he averaged just 5.8 points, 4.3 rebounds and 2.1 blocks per game as a sophomore, Smith emerged as a potential impact player toward the end of the 2012-13 season.
Entering this season, coach Tommy Amaker had hoped Smith could play a key role as the Crimson looked to win the Ivy League outright and return to the NCAA tournament for a third straight season.
Harvard (16-3, 3-0 Ivy) beat Princeton (12-4, 0-2) on Friday. It will take on Penn on Saturday.
A Harvard source said Travis has a concussion, while Okolie is dealing with a sore knee.
The 6-6, 225-pound Travis is averaging 5.8 points (seventh on the team) and 4.2 rebounds (fourth) in 15.3 minutes a game, and the 6-8, 205-pound Okolie is averaging 3.1 points, 1.9 rebounds in 10.1 minutes a game.