Randle, the Lakers' top draft choice this past June, suffered the injury in Tuesday's season-opening loss to the Houston Rockets.
The 6-foot-9 Randle was diagnosed with a fractured tibia.
Randle, the 19-year-old former University of Kentucky standout who was selected seventh overall in June, was driving to the basket when his right foot buckled and he collapsed on the court. Scott said he was told that other players heard a "pop" when Randle went down.
ESPNLosAngeles.com's Baxter Holmes contributed to this report.