Per ESPN's Adrian Wojnarowski, Rondo is expected to miss three-to-five weeks with the injury.
Lakers head coach Luke Walton said he believes Rondo suffered the injury while making a steal during the fourth quarter of Wednesday's 126-117 win over the Portland Trail Blazers, according to ESPN's Dave McMenamin and Youngmisuk.
The 32-year-old Rondo signed a one-year deal with the Lakers during the offseason after spending the previous campaign with the New Orleans Pelicans.
Rondo has now played for six different teams over the past five seasons after spending the first nine years of his career with the Boston Celtics.
He has primarily come off the bench this season as Lonzo Ball's backup, and the four-time All-Star has thrived in that role.
Rondo is averaging 8.5 points, 6.5 assists and 4.5 rebounds per game, while shooting 45.5 percent from the floor and a career-best 42.9 percent from three-point range.
Along with LeBron James and JaVale McGee, Rondo brought some much needed experience and a championship resume to a young Lakers team, as he won the NBA title with Boston in 2008.
Ball will continue to receive the bulk of the minutes at point guard with Rondo out, but Lance Stephenson figures to see more minutes and ball-handling responsibility as well.
The 8-6 Lakers' first taste of life without Rondo will come Saturday when they face the 7-8 Orlando Magic on the road.