Randle, 19, should make a full recovery from the broken leg he sustained in Tuesday's season-opener, according to the person.
Randle was driving toward the basket midway through the fourth quarter when he planted awkwardly and collided with two Houston Rockets players. He stayed on the court for several minutes and was taken off via stretcher.
Randle, the seventh overall pick in this year's draft, had two points when he left the game. The Lakers lost, 108-90, in front of a Staples Center crowd that became suddenly silent after gleefully jeering Dwight Howard much of the night.
Ed Davis can expect to pick up many of Randle's minutes at backup power forward.
With veteran guard Steve Nash already out for the season because of chronic back problems, the Lakers could file another disabled-player exception with the NBA that would give them an additional $1.5 million in spending power. They would receive about $4.9 million to spend on a free agent or a player via trade if they were granted a disabled-player exception for Nash.
If the Lakers experience one more extended injury in addition to Nash, Randle and Nick Young, they could ask the NBA to extend their roster to 16 players via the rarely used "hardship" rule.
When Young returns from a torn thumb ligament, the Lakers would have to go back to 15 players. He is expected to return near the end of November.
Times correspondent Eric Pincus contributed to this report.