The 6-3 Bills were due to host the 3-6 Browns on Sunday at Highmark Stadium, but it has now been moved to Ford Field due to "public safety concerns".
The National Weather Service has issued a lake-effect storm warning lasting until Saturday morning, with estimates suggesting up to six feet of snow could fall in upstate New York in the coming days.
It means Buffalo will now play back-to-back games at Ford Field, as they are due to face the Detroit Lions on Thanksgiving just four days later.
A statement released by the NFL on Thursday confirmed: "Due to public safety concerns and out of an abundance of caution in light of the ongoing weather emergency in western New York, Sunday's Cleveland Browns-Buffalo Bills game will be moved to Ford Field in Detroit at 1 p.m. ET, the NFL announced today.
"The decision to move the game from Highmark Stadium in Orchard Park, NY was done in consultation with the Buffalo Bills and local and state authorities as the region prepares for the storm."