The tech giant are offering to fix the problem with the functionality of the touch screen of the model if users are having difficulty with the whole or "some" parts of the display.
However, they ask that the phone has no other issues before customers bring the device into store or send it away to be repaired.
A message on the official Apple website reads: "Apple has determined that some iPhone X displays may experience touch issues due to a component that might fail on the display module. An affected device may exhibit the following:
"The display, or part of the display, does not respond or responds intermittently to touch
The display reacts even though it was not touched.
"Apple or an Apple Authorized Service Provider will replace the display module on eligible devices, free of charge.
"No other iPhone models are part of this program."
The technical blow comes after it was reported Apple has sold less iPhones than expected.
The firm also explained it expected poor revenue results for the upcoming December quarter.
Meanwhile, the company has also confirmed it will no longer give details of unit sales for its major devices - including iPhones, iPads and Macs.
Although iPhone revenue has soared, it appears the sales figures have fallen short of what was predicted.
The initial results saw Apple shares drop around 4 per cent, and then there was a further decline - more than 7 per cent - after the earnings call revealing the new reporting structure.
Earlier this month, Apple revealed it had sold 46.9 million over the quarter ending September 29, which was similar to last year's 46.7 million.
However, the price boost appears to be helping the company as iPhone revenue rose 29 per cent to $37.2 billion.