Microsoft has not revealed how many of its machines have suffered the problem, but said the number was "bigger than we are comfortable with."
It added that the move - which will also see some people reimbursed for postage and repairs on consoles which were out of warranty - was aimed at keeping the loyalty of its customers.
"The majority of Xbox 360 owners are having a great experience with their console and have from day one," said Robbie Bach, president of Microsoft's Entertainment & Devices Division.
"But this problem has caused frustration for some of our customers and for that, we sincerely apologise."
It added its Xbox division was still expected to make a profit during the financial year beginning 1 July 2007.
Migration manoeuvre
Separately the company has announced an October launch of its advanced version of the Xbox - the Xbox 360 Elite - in Japan, where it lags behind Nintendo and Sony in the console market.
And the company has also unveiled plans to open a software development centre in Canada which it said was a way of hiring talented people from abroad who would struggle to obtain a US working visa.
The Vancouver location would "allow the company to continue to recruit and retain highly skilled people affected by the immigration issues in the US", Microsoft said.