The Serbian's injury is more serious than first thought but the Red Devils expect to have the England international back in contention for the visit of the Gunners to Old Trafford
The duo picked up knocks in the Red Devils' 2-1 win over West Brom on Sunday, and the United boss has now confirmed that Vidic's calf problem is worse than first feared.
He told the club's official website: "Last week we thought Rio's hamstring would have him out for six weeks and with Vidic, we thought it was just a nerve problem. That's reversed itself.
"Vidic has got a calf muscle injury, which means he'll be four to five weeks. It's longer than we thought.
"Meanwhile, Rio's injury isn't as bad as we thought and he could be ready for our game against Arsenal. I don't think he'll be ready for Monday. It's amazing how circumstances can change in a few days."
Sir Alex also spoke of a training ground injury that will keep Rafael da Silva out of action for the long-term, adding: "Rafael has had an operation [on his shoulder] this week and will be out for 10 weeks.
"It was a freak injury really. He won a tackle, stumbled and fell on his shoulder."
As for the remainder of his squad, the Scot is boosted this week by the return of four of last year's integral squad members to training.
He continued: "Patrice [Evra] is back which gives us experience. Chicharito is back training and doing very well as is [Antonio] Valencia who will play in the Reserves next week.
"When will we bring Chicharito back? It depends. From a medical point of view, considering he had a concussion before, we have to decide when is the best time to bring him back.
"Darren Fletcher had a game the other night, so he's back and doing well. He'll play maybe one more game in the Reserves and then should be ready for the first team. So there are a few there, but they're all on the mend, we hope."