Boateng broke the toe in the first half against his former club Aston Villa last Saturday but stayed on the pitch for the entire 90 minutes.
"It is a huge disappointment," said Boateng's manager Steve McClaren. "He has been our player of the season so far. It leaves us thin in midfield."
The Brazilian Doriva is likely to replace Boateng initially, at Birmingham City on Sunday, and with Ray Parlour returning from injury Middlesbrough should have enough cover for the visit of United.