But the unshaven frontman denied he was a lightweight, pleading that he was allergic to salicylates, chemicals found in wine which he claimed made his head "'swell up like a balloon and pop" or make him "fall asleep anywhere."
"The 44th president of the United States — he mixes cocktails," Bono insisted. "He doesn't have too many, he's very measured," he added. "He does make strong cocktails, though, just saying."
The Irish pop star and self-appointed global humanitarian envoy told the anecdote in an interview on Tuesday.
Bono and his wife Ali Hewson had been attending a dinner at the presidential mansion with the then-president, where they mixed red wine with Obama's cocktails.
He soon found himself "slipping off for a kip" in the Lincoln Bedroom, part of the guest suite at the White House and which the Civil War-era president used as his office.
When Obama asked the singer's wife where he had gone, she replied: "He's just gone for a sleep."
"He just has to go for these sleeps, he'll be back in 10 minutes. I've been with him for 30 years, don't you worry a thing about him, Mr. President. I'll go find him," Ali said, according to Bono.
But Obama, recalling that they had been discussing Lincoln earlier, thought to look in the dead president's room. "He just woke me up and laughed. President laughed his head off," Bono said.
Since then, Obama has been boasting how he out-drank the Irish rocker. "He does tell people that he drinks me under the table, he doesn't believe the allergy thing," Bono said.