The council said there was no evidence the house was unstable and that the occupier has been moved into alternative accommodation.
Four cars collided on St Johns Street at around 5.50pm on Tuesday, causing one to hit a house on the street.
The one-way street, which is adjacent to Cann Hall Road, was cordoned off on Wednesday and diversions meant traffic in the area remained substantial in the morning.
One local resident feared the foundation of the house had "come away", rendering the house vulnerable to collapse.
Local resident Katherine Louise McEvilly was walked home by a fireman and fears for the safety of herself and fellow residents after the crash.
She said: "Inspectors and police were in the house checking no one else was in there. It is a risk now, as the foundation has come away and could collapse, so they've used a metal fence to block it off.
"It's of course a bad accident but as far as I know, when I walked down St Johns Street, everyone involved in that accident was OK, just shaken up.
"All I ask is something gets done about St Johns Street as it's very dangerous for us residents."
St Johns Street leads to the bridge over the River Severn in Low Town, and Katherine believes work done on the bridge since river levels have risen over the past week played a part in the collision.
Katherine added: "I walked over the bridge last night and bear in mind for days now since the river has risen there has been work done on the bridge.
"That's causing chaos with traffic both ways and with public walkways, as there are posts blocking us from walking there."
A Shropshire Council spokesperson said: "At approximately 7pm yesterday Shropshire Council’s Building Control team was notified of a vehicle collision with a structure on St Johns Street in Bridgnorth.
"Our local surveyor attended the scene shortly after and assessed the structure, and in conjunction with our colleagues from Shropshire Highways took the decision to close the road to ensure the safety of the public. The occupier of the property was uninjured and is staying in alternative accommodation.
"The owners and their insurers are seeking the advice of a structural engineer to confirm if the damaged elements of the structure require support. There are no indications that the foundations of the property have become unstable, or that the damage inflicted by the vehicle became worse once the vehicle was removed.
"As soon as we are confident that there is no danger to the public the road can be reopened."
A West Mercia Police spokesperson said: "At around 5.50pm on Tuesday 17 January officers received a report of a collision involving four cars on St Johns Street in Bridgnorth. Shropshire Fire and Rescue Service also attended the scene along with council colleagues due to a building being struck by one of the vehicles. None of those involved in the collision were injured."