The city council said it was installing the safety equipment "to provide extra reassurance to residents".
Tenants will be consulted about the work later this year.
The authority also said exterior cladding used on the flats was "fireproof and complies with building and planning regulations".
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In a statement, the council said: "Twenty-one of the council's 24 tower blocks have metal cladding.
"This is fireproof as the insulation is mineral and rock wool, with fire breaks at the floor and party walls. This creates a fireproof box around each flat to the external structure to prevent the spread of fire to other flats.
"The other three are brickwork-clad and designed to operate in the same way as the other 21 but in these cases have a separate metal fire barrier installed."
All 24 council tower blocks in Sheffield will be fitted with sprinkler systems following the Grenfell Tower fire in London.