Vehicles will not be able to turn left from Exeter Street into Bretonside from Monday 4 September.
Local electricity company Western Power Distribution needs to close a section of the road to repair a faulty oil filled cable.
The road will be closed on the westbound (inbound) side only, from Exeter Street to Hawkers Avenue. A clearly signed diversion route will be in place.
The work is expected to take between four and 10 weeks, depending on the severity of the cable damage.