There is no indication as to how many units are faulty, but Apple states that the screen "does not respond or responds intermittently to touch", or that the display reacts "even though it was not touched".
The £999 handset, which was released last November and discontinued in September, has been plagued by complaints from users that its touch screen was not working properly for several months.
The fix offers are the latest in a string of product quality problems over the past year even as Apple has raised prices for most of its laptops, tablets and phones to new heights.
Apple also said a "limited number" of 13-inch MacBook Pros have "an issue that may result in data loss and failure of the drive". The issue impacts some units sold between June 2017 and June 2018.
Eligible devices will be serviced by Apple or Apple Authorized Service Providers for free. However, in this case, doing so will reformat the storage so it's key to backup your data before getting the laptop serviced.
13-inch non Touch Bar MacBook Pro owners who believe they've experienced this issue can check whether they're eligible for repairs on Apple's service program page. If it is, customers should back up their data and then contact Apple or make an appointment at an Apple Store/Authorized Service Provider to get the fix.