The closure, expected to last a maximum of five days, is needed to enable a sewer connection to a new block at Hereford Cathedral School.
Clive Hall, Herefordshire Council's highway network manager, said: "We have required the developer to carry out this work during half-term to minimise disruption to motorists.
"Access will still be allowed with traffic flow on Offa Street being reversed during the duration of the works. This was agreed after holding discussions with Marks & Spencer who need access for deliveries," he added.
Traffic between Offa Street and the closure point, east of the Town Hall will be allowed access but will be required to return to Offa Street. Ferrers Street/East Street (beyond the closure) will remain as it is.