At the December meeting of the school's Athletic Council, Gordon Gee also took shots at schools in the Southeastern Conference and the University of Louisville, according to the recording, obtained by The Associated Press under a public records request.
The university called the statements inappropriate and said Gee is undergoing a "remediation plan" because of the remarks.
Gee apologized in a statement released to the AP.
"The comments I made were just plain wrong, and in no way do they reflect what the university stands for," he said. "They were a poor attempt at humor and entirely inappropriate."
When asked by a questioner how to respond to SEC fans who say the Big Ten can't count because it now has 14 members, Gee said, "You tell the SEC when they can learn to read and write, then they can figure out what we're doing."
The top goal of Big Ten presidents is to "make certain that we have institutions of like-minded academic integrity," Gee said. "So you won't see us adding Louisville," a member of the Big East conference that is joining the ACC.
After a pause followed by laughter from the audience, Gee added that the Big Ten wouldn't add the University of Kentucky, either.
Gee, who has taken heat previously for uncouth remarks, told members of the council that he negotiated with Notre Dame officials during his first term at Ohio State, which began more than two decades ago.
"The fathers are holy on Sunday, and they're holy hell on the rest of the week," Gee said to laughter at the Dec. 5 meeting attended by Athletic Director Gene Smith and several other athletic department members, along with professors and students.
"You just can't trust those damn Catholics on a Thursday or a Friday, and so, literally, I can say that," said Gee, a Mormon.
The Big Ten had for years courted Notre Dame, but the school resisted, seeking to retain its independent status in college football. The school announced in September that it would join the Atlantic Coast Conference in all sports except football. It also agreed to play five football games each year against ACC teams.
In the recording, Gee referred specifically to dealing with the Rev. Ned Joyce, Notre Dame's longtime chief financial officer, who died in 2004.
"Father Joyce was one of those people who ran the university for many, many years," Gee said.
Gee said the Atlantic Coast Conference added Notre Dame at a time when it was feeling vulnerable.
"Notre Dame wanted to have its cake and eat it, too," Gee said, according to the recording and a copy of the meeting's minutes.
Gee took a swipe at Big Ten Commissioner Jim Delaney, one of the most powerful leaders in college athletics, when he answered a question about preserving Ohio State's financial interests in light of Big Ten revenue-sharing plans.
"No one admires Jim Delaney more than I do — I chaired the committee that brought him here," Gee said. "Jim is very aggressive, and we need to make certain he keeps his hands out of our pockets while we support him."