The former England captain was expected to be ruled out for up to six weeks after suffering a hamstring strain in the Red Devils' 2-1 victory over West Bromwich Albion at the weekend.
Despite initial fears, the 32-year-old is expected to return against Arsenal at the end of the month while his defensive partner Vidic could miss up to five weeks with a calf injury.
"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," Ferguson told reporters.
"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."
Meanwhile, the Red Devils manager confirmed that Rafael underwent surgery on a "freak" shoulder injury.
"Rafael has had an operation [on his shoulder] this week and will be out for 10 weeks," he added. "It was a freak injury really. He won a tackle [in training], stumbled and fell on his shoulder."
United defender Patrice Evra is expected to make his return at Old Trafford against Tottenham on August 22.