Randle sustained the injury against the Houston Rockets on Tuesday night in his first ever NBA game, and the seventh overall pick in the 2014 Draft will now be sidelined for the rest of the campaign.
"I didn't get a whole lot of sleep just thinking about the young fella," Lakers coach Byron Scott told reporters.
"[I was] talking to him after the game, basically just holding him and listening to him cry and trying to console him as much as possible. It's a tough situation."
The 19-year-old drove to the basket in the fourth quarter but planted his right foot awkwardly and collapsed before being taken off the court on a stretcher.
Randle is the second Lakers player to be ruled out for the season after veteran point guard Steve Nash saw a back injury end his involvement.