Rondo has missed the Lakers' last 12 games and was also out for 17 contests earlier in the season after undergoing a procedure to repair a fracture in the same hand.
The eventual return of the 32-year-old will give L.A. an additional playmaker behind starting point guard Lonzo Ball.
Los Angeles remains without superstar forward LeBron James, who suffered a groin injury during the Lakers' 127-101 win over the Golden State Warriors on Christmas Day. The four-time MVP has been cleared to begin practicing next week.
Rondo is averaging 8.4 points and 6.7 assists in 14 appearances.