The timetable would keep Rondo out of his team's next two games, including a showdown against the Houston Rockets on Saturday.
The four-time All-Star suffered a nondisplaced volar plate avulsion fracture to his right ring finger in Saturday's victory over the Oklahoma City Thunder.
Rondo signed a two-year, $5.1-million contract with the Lakers this past summer, which includes a $2.6-million player option for next season. The 33-year-old is averaging 7.6 points and is second on the team with 5.4 assists per contest.
Anthony Davis also missed Monday's game against the Cleveland Cavaliers with a bruised backside. Head coach Frank Vogel says the Lakers superstar is "day-to-day."