The road will be shut to traffic between Samos Road and Weighton Road from Thursday, June 12, at 8pm until Saturday at 6pm.
The closure is part of preparation for the emergency demolition of a building, which is set to begin next week.
During this period, diversions for all vehicles, including buses, will be in place.
The initial work includes putting up hoardings to keep the wider area safe during the demolition process.
TT Pharmacy, located on Croydon Road, is expected to be closed during the road closure period.
Residents are advised to use alternative pharmacies, with locations available on the NHS website.
Croydon Road is expected to partially reopen on Saturday, June 14, at 8pm, with temporary traffic lights controlling the flow of vehicles.
Due to the extensive hoarding work, the road will be narrowed.
A temporary crossing will also be installed for pedestrians.
Three local bus stops will remain closed for the entire duration of the demolition work.
Tremaine Road, at the junction with Croydon Road, will also be closed for the length of the demolition process, which is anticipated to take about three weeks.
The decision to demolish the building comes after it was reported last year that the structure of the former Mitre public house had become unstable during construction work, leading to the emergency evacuation of local residents.
Recent expert monitoring of the adjacent buildings, which are part of the same block and have been supported by scaffolding, has shown further cracking and increased instability, making them dangerous.
As a result, the council has decided to demolish the buildings to ensure public safety.
A Bromley Council spokesperson said: “This demolition work is an absolute last resort, with our structural engineers advising that the building has become even more unstable and is now dangerous.
“The road is closed to allow for preparation work, with a hoarding being erected around the building, with demolition work then getting underway.
“Croydon Road will partially reopen once the hoarding is constructed and only fully reopen once the demolition work is complete.
“We apologise for any inconvenience, with this work unavoidable from a safety perspective.”
