Veolia workers, who are members of GMB Union, staged a walkout between 6.30am and 10.30am, as part of an ongoing dispute about pay.
The union has demanded a 3 per cent pay increase and said industrial action will continue every Monday until a new deal is agreed.
GMB organiser Lee Parkinson said the workers have gone “above and beyond” during the pandemic and they want a “decent pay rise that at least keeps pace with the cost of living”.
The union also claims up to 200,000 homes will face disruption caused by the strike, but Veolia has disputed this figure.
The company said workers recently voted to reject an “improved deal” and it is “disappointed” that they have decided to take industrial action.
A spokesman said: “This will affect up to 40,000 properties.
“We continue to engage with our colleagues and GMB representatives and we are working to minimise any disruption to residents’ recycling and waste services.
“We will provide further information to residents regarding changes to bin collections and would like to apologise for the inconvenience this will cause.”
In a statement, GMB said: "Members at Veolia Sheffield have voted to strike over pay and ongoing attacks to their terms and conditions.
"Refuse workers have kept the city going during the pandemic. After of decade of Government austerity they deserve a proper pay rise."