According to the club's website (www.manutd.com) on Wednesday, Van der Sar underwent surgery on his left hand after injuring it saving a penalty from Danijel Pranjic in United's shoot-out defeat to Bayern Munich in a pre-season friendly.
"He will be out for up to eight weeks," the club said. "The prognosis means that Van der Sar won't be back to full fitness until the end of September."
Van der Sar was instrumental in United's 18th league title last season, setting a new English record of 14 consecutive league clean sheets.
The 38-year-old's injury means Ben Foster, who signed a new contract in July, could get the chance to impress, starting with this weekend's curtain-raiser against Chelsea in the Community Shield at Wembley. Tomasz Kuszczak is also in reserve.