Mike Bresnahan of the Los Angeles Times reports that Randle is expected to make a full recovery after having surgery Wednesday morning.
Randle was the No. 7 pick in May's draft after one season at Kentucky. The 19-year-old averaged 15 points and 10.4 rebounds per game as a freshman for the Wildcats.
On Thursday, the Lakers announced that 40-year-old point guard Steve Nash will miss the entire season due to recurring nerve damage in his back. Los Angeles is also currently without Nick Young, who had surgery on his thumb on Oct. 6 and was expected to miss eight weeks.
The Rockets won Tuesday's opener 108-90. The Lakers play the Suns in Phoenix on Wednesday.