Young is expected to undergo an MRI on Wednesday in Chicago, ahead of the Lakers' matchup with the Bulls, according to the team.
"It will be tough," Lakers coach Luke Walton said. "Without breaking up that second unit -- the filling in the shooting guard spot while D'Angelo [Russell] is already hurt -- we'll have to get creative."
The 31-year-old Young did not put weight on his right leg as he was carried into the locker room on the arms of two teammates after suffering the injury in the first quarter.
After contesting a fast-break layup by the Pelicans' Tim Frazier with 10:18 to play in the quarter, Young hopped on his left leg around the baseline before collapsing in front of the scorer's table. Timeout was called as Young grabbed at his right foot in apparent pain. Young was attended to by a member of the Lakers' training staff before being carried into the locker room.
Young has undergone a mild resurgence in his fourth season with the Lakers. The 10-year veteran has started all 18 games in which he has played and is averaging 14.1 points per game and a career-high 41.8 percent from the 3-point arc in his first season under Walton.
ESPN's Baxter Holmes and The Associated Press contributed to this report.