The veteran Welshman was replaced by Dimitar Berbatov and left the stadium with his right arm in a sling, with Ferguson confirming the hospital appointment.
"We have sent Ryan for an X-ray to see if there is any damage," said Ferguson.
"It is very painful but hopefully he is going to be all right."
Giggs had already played a major role in United's equaliser, driving a low cross-shot into the Villa box that was turned into his own net by James Collins.
Remarkably, it was the 10th own goal United have benefited from this season - second only to Rooney in the scoring charts - and it allowed them to close the gap on leaders Chelsea to a single point following their surprise defeat at Everton, the Red Devils' next Premier League opponents.
"We have gained," said Ferguson.
"It was an important night and, with Everton winning against Chelsea, we have gained one point and one goal.
"It could be important point."
The own goal cancelled out an earlier effort from Carlos Cuellar, with Ferguson claiming his side were the ones who looked most like collecting maximum points after half-time.
That was despite United being forced to play with 10 men for the final hour after winger Nani was sent off for a woeful tackle on Villa skipper Stiliyan Petrov.
Although Ferguson complained United should have had a free-kick immediately before the incident for a Gabriel Agbonlahor tackle on Wes Brown, the Scot had no argument with Peter Walton's decision to show Nani a red card that will rule him out of the Carling Cup finalbetween the two sides at Wembley on February 28.
"It was a sending off," said the United boss of his side's sixth dismissal of the season.
"It was a red card. It was a naive tackle.
"He is not a malicious player but he has gone in with his foot raised off the ground and we cannot complain about it.
"We should have had a foul seconds before when Agbonlahor came in with his foot up on Wes Brown's ribs.
"That was disappointing but we have no argument at all with the red card."
Villa manager Martin O'Neill felt his side failed to cash in on their one-man advantage after the sending-off of Nani.
But he remains optimistic Villa will head to Wembley full of confidence for the Carling Cup final.
O'Neill said: "When United had a man sent off, I was hoping we could take the initiative, but in the second half we didn't create enough or take advantage of the extra man.
"But then we were up against a quality side who have been in situations like that before, so, from that viewpoint, we could learn a bit.
"But, if you had said at the start of the season that we would take four points off United, then I would have been happy. And, when Wembley comes around, we should still go into the game full of confidence.
"There were more than glimpses out there of why Manchester United are such a fine side and have been the champions three times running."
Meanwhile O'Neill revealed Stiliyan Petrov is doubtful for Sunday's FA Cup tie at Crystal Palace after being injured in the challenge by Nani which saw him red-carded.
The Bulgarian player was limping when he left Villa Park with an ankle knock.
O'Neill said: "He is pretty sore at the moment. He thought at half-time that he would be okay but it stiffened up.
"I don't know about Sunday's game yet but I would think there is some doubt about whether he will be fit."
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