Complaints about the iPod nano surfaced on the internet with owners complaining about cracked screens and easily-scratched surfaces.
The iPod nano was launched with great fanfare earlier this month, billed as the music system which is thinner than a pencil.
Each iPod nano, on sale for £179, holds up to 1,000 songs or 25,000 photographs.
It was described as an "impossibly small size" which could fit into the smallest pocket.
But complaints about the product grew to such an extent that a website was set up by disgruntled owner Matthew Peterson entitled flawedmusicplayer.com.
He invited other iPod nano owners to air their views and posted pictures of cracked screens on the net.
Today Apple conceded that there had been a problem with the iPod nano but insisted it was not a design flaw.
Phil Schiller, from Apple, said: "This is a real but minor issue involving a vendor quality problem in a small number of units.
"In fact, this issue has affected less than one tenth of 1% of the total iPod nano units that we've shipped. It is not a design issue."
He said any iPod nano owners who found their screens were cracked would get their music player replaced free of charge.
Referring to the alleged easy scratching, Mr Schiller said the product was made out of the same material as Apple's white fourth generation iPod which had received no complaints.
"We have received very few calls from customers reporting this problem - we do not think this is a widespread issue," he said.
"If customers are concerned about scratching, we suggest they use one of the many iPod nano cases to protect their iPod."
Mr Peterson posted a response on his flawedmusicplayer.com site welcoming Apple's stance.
He wrote: "I am very delighted to see Apple take this issue seriously. It is sad that it took a website and a lot of publicity before they finally investigated but at least future nano users with the same problem I had will not be subjected to the same treatment that I was.
"This was a real issue and most people tried to ignore it. I know a lot of people are going to complain that they still have to spend extra money on a case to prevent scratching.
"I guess I can handle using an iPod sock on my nano knowing that I can look at my screen and show someone a picture. Thank you Apple."