Durant, 28, limped out of Tuesday's game after team-mate Zaza Pachulia fell on his left leg and caused a sprained medial ligament and leg bruising.
It is hoped he could return before the end of the regular season on 12 April.
The 2014 NBA Most Valuable Player joined the Warriors this season in a deal worth a reported $54.3m (£43.9m).
Durant had spent the previous eight seasons at Oklahoma City Thunder, where he was a four-time NBA scoring champion.
Western Conference leaders Warriors went into the game with a league-best 50-9 record and have already booked their place in the play-offs.
Golden State Warriors' top scorer Kevin Durant will be out "indefinitely" after injuring his knee in his side's 112-108 loss at Washington Wizards.