In a posting on its support site, the technology giant says the issue affects handsets “sold between September 2012 and January 2013 and fall within a limited serial number range.”
Affected handsets will qualify for a free replacement battery.
The repair programme is now open for US and China and will be available in other countries as of August 29, 2014.
As is standard for the firm’s replacement programmes, any other damage, such as cracked screens, will need to be repaired before the new battery will be fitted.
In most cases there would be a charge for this extra work.
To check your phone’s eligibility, visit apple.com.