The stone carving, which had formed the top of a pinnacle, fell from St Mary the Virgin church in the early hours.
St Mary's Place, which is next to the redundant church, has been sealed off while safety checks are carried out.
Robert Milton, from the Churches Conservation Trust which looks after the grade I listed building, said the damage was caused by adverse weather.
He said the top of the pinnacle, which is an early Victorian addition, had fallen from the chapel at the rear of the church.
"Quite a bit of it smashed so parts will have to be replaced. I expect it will cost about Â£10,000 to repair. At least that," he said.
Mr Milton said the church, the only complete medieval church in Shrewsbury, was "incredibly important" as a listed building and to the trust which protects 346 churches which are no longer used for worship.
St Mary's, which has not been used for regular church services since 1987, is used for exhibitions, concerts and events and also has cafe.
It will also be the site of the town's first chocolate festival next month, he said.
Mr Milton believed the rest of the church site was safe, but said it was due to be checked by architects.
A 4ft (1.2m) tall ornate carving has fallen from a medieval church in Shrewsbury town centre.