The 33-year-old O'Hara was sent from training camp at the University at Albany to the Hospital for Special Surgery in New York City on Tuesday for an MRI.
The examination revealed no new injury to the ankle. The swelling, however, is the result of a chronic condition in the joint.
Doctors and trainers will try to reduce the swelling so O'Hara can regain mobility, the Giants said.
The Giants also disclosed on Tuesday that receiver Hakeem Nicks, their first-round draft choice last season, hyperextended his right knee at the end of practice. He will undergo an MRI and be examined on Wednesday.
The Giants do not expect to update his status until Thursday.
O'Hara took part in conditioning drills Sunday morning and a light workout that afternoon. He did not appear to hurt the ankle at any time.
Swelling developed in the ankle late Sunday and he has missed four practices over the past two days at the University at Albany.
"I definitely think there is some uncertainty," said guard Chris Snee, who also has played in the last two Pro Bowls. "We can't worry about that. Shaun is going to do whatever he can to get back on the field. Right now, we will go with who we have out there and just really work on that continuity."
O'Hara has started all but five regular-season games at center since joining the Giants as a free agent in 2004. Four of the games he missed came in that first season with the other coming in 2006.
The former Rutgers player who has been selected to the Pro Bowl the past two years has started every regular season game since 2007. He only game he missed in the past three seasons was the NFC Wild Card game in 2007 in New York's run to a Super Bowl title.
Adam Koets, who has played in has three regular season games in his first three years in the league, has taken over at center in O'Hara's absence.
"Everyone wants to play," Koets said between practices on Tuesday. "It is an opportunity for me and I just have to make the most of it."
Drafted as a tackle out of Oregon State in sixth round in 2007, Koets has never started an NFL game. He appears to have put on muscle in the offseason and seemingly has not made the blatant errors that had coaches all over him earlier in his career.
"I kind of realized I have been here three years and it's time for me to step up and play," said Koets, who can play any position on the line. "It's an opportunity for me I have to show what I can do."
Veteran Rich Seubert, who is fighting for his job at left guard, also has gotten more work at center the past two days.
He downplayed the ankle injury on Monday, saying O'Hara will be fine.
"We all like to take a couple of days off from practice," Seubert said. "I did last year for a couple of weeks. It's O-Line humor. He'll be fine. One thing you don't have to worry about, unless we're at the hospital laying down and they are tying you down, you're going to try to get out there as soon as you can. We all know Shaun would rather be out there practicing."
The Nicks' injury also is causing some concern. Fellow receiver Mario Manningham injured his groin in practice, leaving the team without their No. 2 and 3 receivers from last season.
Manningham had 57 catches for 822 yards and five touchdowns. Nicks had 47 receptions for 790 yards and six TDs. Steve Smith led the team with 107 catches for 1,220 yards and 7 TDs.