A stone pillar on a 19th Century former bridge tollhouse was destroyed when it was hit by a car.
The Grade II*-listed building on Bath's Cleveland Bridge was hit at about 01:30 BST, Avon and Somerset Police said.
Bath and North East Somerset Council said the tollhouse had sustained "significant" damage, but the bridge remained "structurally sound".
The road was earlier closed in both directions and motorists have been advised to avoid the area.
Police said inquiries were continuing after the car became embedded in the building and its occupants left the scene.
Engineers have now re-opened one lane under temporary traffic lights, and this is likely to remain in place throughout Monday's rush hour, the council said.
The bridge over the River Avon was built in 1827 and is described by Historic England as "among the most characteristic examples of a Greek Revival bridge".
History of the bridge and tollhouse
- Cleveland Bridge was built in 1827, reconstructed in 1928 and strengthened in 1992
- It cost £10,000 and was for the Earl of Darlington who owned the Bathwick estate
- The tollhouses are in the form of small Doric temples, based on Greek architecture
- The bridge tolls were scrapped in 1929
Source: Historic England