Some users say the drive is making very loud noises when they try to insert a disc and in some cases is not reading discs at all.
Microsoft says only a very small number of users are affected.
The Xbox One was launched on November 22 and sold more than one million units in the first 24 hours.
More than 150 people contacted Kotaku, a gaming news website, claiming their new consoles were faulty. Other users uploaded videos apparently showing the problem to the gaming forum NeoGAF.
“The issue is affecting a very small number of Xbox One customers,” said Microsoft in a statement.
“We’re working directly with those affected to get a replacement console to them as soon as possible through our advance exchange programme.”
The Xbox One is the first new console from Microsoft in eight years and it broke all previous Xbox first-day sales records when it went on sale last week.
Microsoft said it had now sold out at most retailers and it was working to replenish stock as fast as possible.
This is not the first time Microsoft has experienced problems with the launch of an Xbox console. When the Xbox 360 was launched in 2005 some users reported faults with the hardware which led to three red lights flashing on the front of the device and the console becoming unusable. The problem became known as the “red ring of death”.
The launch of the Xbox One came a week after the US launch of Sony’s PlayStation 4. The two consoles are set to go head-to-head in the crucial Christmas season.
The PS4 also experienced technical issues after its launch with users complaining that a blue light continually flashed on the console affecting its operation and others reporting that sometimes the unit suddenly turned itself off.
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