Ferdinand was forced to pull out with a thigh injury, with Ferguson claiming before the game that his £29.1million defender will be going for a scan in the morning.
However, the United boss has now put a timescale on the problem, which would make the 30-year-old a doubt for England's World Cup qualifier against Croatia on September 9.
"I would imagine Rio will be out for two weeks," said Ferguson.
With Nemanja Vidic already sidelined and Jonny Evans limping out of Sunday afternoon's 1-0 win over Birmingham, Ferguson is short of defensive cover ahead of Wednesday's trip to another newly-promoted side, Burnley.
At least Ferguson knows his attack is clicking into gear, with Wayne Rooney
following up his goal in last week's Community Shield by tapping home the match-winner after his own header had bounced straight back into his path off a post.
"He took it very well," said Ferguson.
"It was a good header to start with and he was very quick to get to the rebound. He reacted in the right way and it gets him on the road to what we hope will be a very significant total for us this season."
Rooney's contribution this season will be crucial because United have to find some way of making up the 30 goals Cristiano Ronaldo has regularly contributed on an annual basis.
"If you have two or three strikers who can get you 20 it stands you in good stead." said Ferguson.
is well capable of that."
There was no argument from Alex McLeish, whose team turned in a creditable performance, without ever quite getting to grips with Rooney's threat.
Discussing Rooney, McLeish said: "We have seen so many natural footballers over the years, people like Zinedine Zidane and Luis Figo, they are difficult to coach.
"You can do one or two things in terms of the shape of the team but when he drops into those little pockets, he is hard to pin down."
As the first manager to send a team out in the post-Cristiano Ronaldo era, McLeish now knows how United have been affected by his departure. The answer is not much.
"There might be certain little things you can pick up on a DVD but Manchester United have such a vast pool of talent they can still cope with most teams in the league," McLeish said.
Birmingham might have picked up a point had it not been for one magnificent late save from Ben Foster to deny Christian Benitez.
However, that would have been a travesty for the hosts, who
dominated possession and chances.
Dimitar Berbatov went close on numerous occasions, with Lee Carsley nodding one header off the line, and the Bulgarian was unlucky not to get a penalty when he was trodden on by Stephen Carr.
His replacement Michael Owen might have had one on his debut as well, only for the former Liverpool forward to fire straight at Joe Hart.
"The more you watch it, the better that save was," said Ferguson.
"Nevertheless, he will get his goal and once he does, it will set him on the road as well."
After drawing their last two opening fixtures against teams - Reading and Newcastle - who were subsequently relegated, at least United were able to get a win this time.
And, while the loss of Ronaldo is going to take some getting used to, Ferguson still feels United can look forward with confidence.
"I know some of our supporters are still worried that I have not bought a megastar to replace Cristiano," he said.
"They are concerned because they can't quite work out how we are going to compensate for all the goals Cristiano used to get for us.
"But I am more than happy with our squad and although we have lost a major player, I believe we are on the threshold of a very exciting era for Manchester United."