The South African No.8 was unable to feature for Saints in Sunday's 23-22 defeat to Bath at Franklin's Gardens, with Tom Wood starting in his place.
And Adendorff, who had scored four tries in his previous three appearances, will not be making a rapid return to action.
Saints boss Chris Boyd explained: "He had a small surgery on a knee and he'll be out for four to six weeks."
But there is better news on another No.8, Teimana Harrison.
Boyd said: "Teimana's probably up for selection this week. He's just about ready to go."
Courtney Lawes was recently ruled out of the remainder of the Six Nations after picking up a pectoral injury in training.
And when asked for an update on the Saints lock, Boyd said: "He's got a specialist appointment and they'll decide exactly what's going on there and give a diagnosis this week."