Skinner Street, The Traverse, Buttermarket and Cornhill are currently closed to vehicles.
There are also road closures on Guildhall Street at the junction with Churchgate Street; Woolhall Street at the junction with St Andrew's Street South; and Abbeygate Street at the junction with Buttermarket.
The town centre remains open to pedestrians, with restrictions on Skinner Street and The Traverse. Most businesses in the area are open as usual.
Fire crews are still at the scene of a major fire at Strada restaurant in Bury St Edmunds on Saturday night.
Part of Bury St Edmunds town centre could be sealed off for most of today (Sunday 17 June) after a blaze at a historic building.