Brown limped out of his side's meeting with West Ham on March 21 and, although initial fears he could miss the rest of the season have been allayed, he will be watching Sunday's clash with arch rivals Newcastle United from the sidelines.
Head coach Dick Advocaat said: "It's difficult to say how long it [Brown's recovery] will take, but it will be at least three weeks."
Midfielder Lee Cattermole will be involved from the start following a two-match suspension, and Advocaat is confident his side can handle the pressure as relegation-threatened Sunderland bid for a fifth straight Tyne-Wear derby win.
"Everybody was back on Thursday and they looked sharp. I think they know exactly what they have to do on Sunday," Advocaat added.
"It's a special game and very important. The most important thing is that we show the crowd we want to win and get them behind us. It is very important for them to support us, and that can be a key factor.
"We all know [how] important this is and it's a special moment for everybody - but it's about getting the result we need."
