Jones, 20, suffered a meniscus tear in training. He had already missed the start of the season due to a back problem.
The news means the England international is likely to miss seven Premier League games as well as the opening three matches of United's Champions League campaign.
A statement from the club read: "Phil Jones has had surgery on a knee meniscus tear sustained in training that will require six to eight weeks of rehabilitation."
United have suffered extensively from injury problems in defence already this season and were forced to start the new campaign with Michael Carrick at centre-back.
Though Nemanja Vidic and Rio Ferdinand are both now fit, along with Jonny Evans, Chris Smalling remains sidelined with a broken metatarsal.
Jones joined United in a £16.5 million deal from Blackburn Rovers last summer and made 29 Premier League appearances in the 2011-12 season.