Cladding on Hanover Tower is being replaced after a survey in the wake of the Grenfell Tower disaster found a single element of covering failed the inspection.
Green councillors quizzed the council about the cost of the new cladding on the tower block at Exeter Drive in Broomhall.
Coun Jim Steinke, Cabinet Member for Housing, said: 'The cost of removal was Â£455,177. The building works reinstatement cost is estimated at Â£2.8m plus fees. The total cost of removal and reinstatement work is Â£3.92 million.
'Financial provision has been made to fund the new cladding from the Housing Revenue Account. A grant submission has been made to national Government for the cladding costs. Sheffield hopes to receive confirmation of the grant this month.'
Coun Steinke said there were no plans to reclaim this money from the original installers.
New, solid metal cladding will replace the panels which have been removed. Work will include the installation of the cladding, including insulation, the replacement of any damaged parts of the frame from which the cladding is suspended and any '˜making good' such as re-sealing around windows.