Division Street will be one-way between Rockingham Lane and Rockingham Street - a section which includes Eton clothing, Pieminster and Bungalows and Bears bar. It will only be open to traffic heading westbound, away from the city centre.
Rockingham Street will also become one-way - from Division Lane to Wellington Street - heading south only.
The restrictions come as another length of Division Street remains closed to traffic under a social distancing order announced in June.
The section outside Lucky Fox and The Copperpot cafes and the Frog and Parrot pub - between Rockingham Street and Westfield Terrace - is for cycles and pedestrians only and featured tables in the road last summer.
A Sheffield Council spokesman said: “The council is making preparations for the start of construction on the Heart of the City masterplan between Cambridge Street and Carver Street, including Leah’s Yard, Bethel Chapel, Cambridge Street Collective and Elshaw House.
"Details of the contractor and the construction programme will be announced in the coming weeks. These measures allow for emergency Covid-19 measures along Leopold Street to continue, while also enabling Heart of the City to continue to progress. The measures are being implemented under a temporary order for 18 months and can be reviewed as required.”
Elshaw House, previously know as Block H2, will be in an area bounded by Wellington Street, Backfields and Carver Street. Plans for a nine-storey office block, with shops and cafes on the ground floor, received planning permission in October.
The application was submitted by Sheffield City Council, which is acting as developer and funder of the £480m Heart of the City scheme.
Meanwhile, the revamp of an office block on Carver Street as part of the HoC2 – which will stand diagonally opposite Block H2 – is nearing completion.
Sheffield Council gave £2m towards the redevelopment of 38 Carver Street in return for a 20-year lease taken out by property management specialists Staton Young.
The five-storey, glass-fronted building will become Cubo, comprising serviced offices, communal areas and a rooftop bar.