The Xbox 360-exclusive platformer apparently crashes at certain stages for some users, has trouble running from a USB stick, and is not compatible with some older models of the console with smaller hard drives.
"A small subset of older Xboxes with smaller hard drives can't run the game at all. The game has trouble running off a USB stick. Crashes are occurring in specific levels or situations," read a statement from the studio.
"In a rare situation (exiting the game from the "wall village" interiors), the save file becomes unusable. Nasty stuff," it went on.
Polytron said that it is working with Microsoft to amend these issues, and said that a patch will likely be released in the future. The corporation encourages users to report glitches as many have "simple workarounds".
The company added: "We will be working internally and with Microsoft on those issues and let you know more later. It makes sense to issue a patch, but we don't currently have an ETA on it."
Fez is available now on Xbox Live Arcade for 800 Microsoft Points (£6.80/$10).
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Watch the launch trailer for Fez below: