Apple didn't say what caused the problem that let many people oversleep on the first two days of the New Year, but said the alarm will work properly on Monday, the BBC reported.
Bloggers and tweeters complained the glitch made them late for work and put them at risk for missing planes and trains.
"We're aware of an issue related to non-repeating alarms set for January 1 or 2," Apple spokeswoman Natalie Harrison said. "Customers can set recurring alarms for those dates and all alarms will work properly beginning January 3."
The anomaly appears to affect single alarm settings on the iPhone 4 and earlier models with software updates, the BBC said.
Apple sold more than 1.7 million iPhone 4's by June 2010, making it the company's most successful product launch.