Reports of screen burn on Google's news Â£799 smartphone
The fault can occur in high resolution screens when an image is displayed for so long that a permanent shadow remains even after the image has changed.
Some early reviewers of the new phone have claimed to have experienced the "burn-in" with icons that are displayed at the bottom of the screen remaining visible even when not displayed.
Technology writer Alex Dobie from Android Central posted an image on Twitter of the fault on his screen, writing "That's some pretty wild OLED burn-in on the Pixel 2 XL after maybe 7 days of full-time use".
"Don't remember the last time I saw burn-in this bad, this quickly on a flagship phone," he said.
The device is due to go on sale in the UK on November 15, starting at £799.
In response, Google said it was investigating the issue.
"We put all of our products through extensive quality testing before launch and in the manufacturing of every unit," the technology giant said in a statement.
"We are actively investigating this report."
The new smartphone - which was unveiled earlier this month - is designed to rival Apple's iPhone and Samsung's Galaxy S and Note flagship devices, and has so far been warmly received by critics.
Last year, Samsung was forced to recall and then discontinue its Galaxy Note 7 after safety issues were discovered with the phone's battery, which in some cases was found to overheat and catch fire.