A portion of a roof on an old brick building next to the First Tennessee Pavilion by Finley Stadium collapsed on Friday.
City public works employees were clearing the rubble and seeking to temporarily stabilize the building.
Officials said steps would be taken to have it completely demolished.
It was part of an old factory once at the site.
The building is jointly owned by the city and county.
No one was injured in the collapse, which comes just after a similar incident at the Cheeburger Cheeburger building at 138 Market St.
The popular Chattanooga Market reopens soon at the First Tennessee Pavilion.