The centre-back suffered a recurrence of the problem in training before last night's 3-0 win over West Ham in the Premier League.
Sir Alex Ferguson had been hoping to have Ferdinand available for the weekend but has now revealed that "he won't be ready" in time to take the field as the domestic league champions go in search of their first silverware of the season.
"He tweaked his back in training," said Ferguson.
"It is unfortunate for him that he's going to miss a couple of games."
Ferdinand was only just coming back from a four-game ban for violent conduct after striking Hull forward Craig Fagan with his arm last month.
And the injury could also prevent him taking the England captain's armband for the first time since replacing John Terry when Fabio Capello's side take on Egypt in a friendly on March 3rd.
"Rio has been training great - there have been no mishaps at all," Ferguson continued.
"But when you get these twinges you can't take a chance."