The team announced the surgery and time frame Tuesday. Orpik has missed the past nine games.
He has a goal and an assist in 10 games this season. He hasn't played since Oct. 27 and was placed on long-term injured reserve Nov. 9.
After helping the Capitals win the Stanley Cup last season, the 38-year-old was traded to Colorado, then bought out and returned to Washington. He signed a one-year deal worth $1 million with a $500,000 bonus for playing 41 games, a total that is in jeopardy because of the injury.
Orpik is in his 16th NHL season. He is eight games from reaching 1,000 for his career.