Fish Street in the town centre is closed to cars from High Street but still open for pedestrians after damage was caused to the Bear Steps building next to St Alkmund's Church.
The road may not be fully back open for nine months, Shropshire Council has warned.
The brown and white timber building, which dates back to the 15th century and is grade II listed, contains an art gallery and cafe and is also home to Shrewsbury Civic Society.
Scaffolding has been put in place to support the building, which is fenced off on Fish Street but unaffected on the St Alkmund's Square side. The art gallery remains open.
A Shropshire Council spokesman said the authority is investigating and that access could be restricted until next year.
The area surrounding Bear Steps contains some of Shrewsbury's most famous and historic lanes, with more than 10 listed buildings on cobbled Fish Street alone.
Just down from Bear Steps is Grope Lane, a narrow street leading to High Street, while St Alkmund's Church is behind and Fish Street leads round to Butcher Row.
A Shropshire Council spokesperson said: “An outline structural assessment of the timber frame of Bear Steps was undertaken yesterday, and investigations are ongoing.
"Whilst the repair programme has yet to be fully considered, it is envisaged that the scale of repair will be significant.
"As a result, we envisage that vehicular access to Fish Street will be restricted for around 6-9 months.”