City officials say the work will mean limited access for both pedestrians and vehicle traffic on South Fourth Avenue between East Third and East Fourth streets Wednesday and Thursday.
The building suffered a partial collapse in early August that took out the side of the structure. The building housed an auto parts and vehicle repair facility, but no one was injured.
The collapse happened early in the morning, and city officials say they believe heavy rain from the night before was the cause.
Pedestrians and drivers are advised to use alternate routes for the next two days while the demolition work is conducted.