Tonnes of rubble came crashing down underneath the road as contractors carried out renovation work to a pub situated in historic arches beneath the route.
Engineers from Brighton and Hove Council are working at the scene to assess the damage.
Council Executive Director Geoff Raw said; “Structural engineers will be working over the weekend to assess the extent of the problem which seems to have been caused by historic alterations to premises in the arches.
“We’re working as swiftly as possible with the police and key partners to ensure public safety and to keep the traffic moving as smoothly as possible.”
Sussex Police have been forced to change the route of a march due to take place in Brighton on Sunday.
The police said: “The A259 eastbound at the junction with West Street was closed around 8am on Friday due to the collapse of a roof of the Fortune of War pub in the King’s Road arches.
“The collapse has lead to a weakness in the eastbound carriageway. Workman discovered the fault and the road was closed while structural engineers assessed the situation.
“Structural engineers have now assessed the road and the eastbound carriageway will remain closed for the next few weeks.”