Ferguson's central-defensive stalwarts both limped off during the second half of the first game of United's Barclays Premier League title defence.
Ferdinand appears the most serious, sidelined for six weeks with a hamstring problem that also means he will miss England's Euro 2012 double-header against Bulgaria and Wales next month, as well as the start of United's latest Champions League quest.
"Rio has a hamstring injury. He will be out for six weeks," said Ferguson.
"With Nemanja, we hope it is a nerve in his calf. He felt it prior to the game but he wanted to play. That may be a couple of weeks."
With young full-back Rafael ruled out for 10 weeks after dislocating his shoulder in training, Ferguson suddenly has a worrying list of defensive problems ahead of a difficult start, that now pits his side against Tottenham and Arsenal at Old Trafford over the next fortnight.
The bright spot for Ferguson is the anticipated return of Patrice Evra from a knee injury against Spurs next Monday.
"We can always put Fabio on the right if we need to. We also have Chris Smalling, so we will get through," said Ferguson.