The first-round Draft pick came under pressure from two Rockets players while looking to shoot late in the 108-90 defeat at the Staples Center, with the team doctor initially diagnosing the 19-year-old with a broken tibia.
Coach Byron Scott told reporters: "It is heartbreaking, because I saw him all summer. I saw the work that he was putting in. I saw the progression that he was making, the steps that he was taking to get better. And his first game, he goes down.
"I don't think anybody in that locker room is happy about the way we played, but we're even more saddened about the fact that we lost one of our young guys.
"I just told him to stay strong. Adversity tests the true character of a man. This is some adversity that we're facing with a young guy being out, and obviously, it's something that he's facing. I feel for him. I feel extremely bad for him. He was kind of crying, and I just told him to stay strong and that it's going to make him a better basketball player."
Randle had three shots during a 14-minute spell on his debut, scoring two points.