The passer-by suffered a minor injury when the rubble fell from the building above a hairdressers in Castle Street, Shrewsbury last Wednesday.
Shropshire Council has said that the building is structurally sound, and the scaffold has gone up to help with remedial work.
Daniel Fox, business support technician with the authority, said: "In reference to the building on Castle Street, the loose material came from a trim around the rooftop of the building and has been removed by an engineer.
"A scaffold has been installed to facilitate any remedial works. The building itself is structurally sound and will not need to be demolished."
The road was closed from around 11.30am until late afternoon after the masonry fell.
The person hit received a "minor injury", Shropshire Council has said.
Police were initially on the scene before the fire service arrived. Pedestrians were able get past but the road was closed to traffic.