The presence of holy teachings within a bathroom environment is seen as offensive to Muslims, prompting Activision to take action.
Apologising for the error, a spokesperson for the Modern Warfare 2 publisher told Kotaku that the map would be taken offline while the team issues an update to remove the texture.
"We apologise to anyone who found this image offensive. Please be assured we were unaware of this issue and that there was no intent to offend," reads the statement.
"We are working as quickly as possible to remove this image and any other similar ones we may find from our various game libraries.
"We are urgently working to release a Title Update to remove the texture from Modern Warfare 3. We are also working to remove the texture from Modern Warfare 2 through a separate Title Update.
"Until the TU is ready, we have removed the Favella multiplayer map from online rotation.
"Activision and our development studios are respectful of diverse cultures and religious beliefs, and sensitive to concerns raised by its loyal game players. We thank our fans for bringing this to our attention," the statement concludes.
Modern Warfare 2 released for the Xbox 360, PS3 and PC in 2009.
The game enjoyed one of the UK's biggest-selling video game launches, topping the all-format chart for Christmas, 2009.
> Read Digital Spy's 'Modern Warfare 2' review
Watch a trailer for Modern Warfare 2 below: