The problem soon picked up the online nickname, the "disc drive of death."
Microsoft says it will replace any defective console, and also offered a free digital game download to affected users.
In a statement released to CBS News, Microsoft said, “The issue is affecting a very small number of Xbox One customers. We’re working directly with those affected to get a replacement console to them as soon as possible through our advance exchange program. Rest assured, we are taking care of our customers.”
The company says it sold more than a million Xbox One consoles in their first 24 hours on the market.
The Xbox is facing tough competition from Sony’s new PlayStation 4, which launched a week earlier and also sold more than a million consoles the first day.