Locals in and around Norfolk Park are angry that a group called the UK Freedom Movement is promoting a gathering which could break laws around social distancing and put people at risk of the coronavirus.
A poster which encourages people to meet at the park on Saturday, as well as at Sheffield’s Encliffe Park, is being shared around social media.
It says: "Join the UK Freedom Movement and be part of the largest mass gathering since the lockdown.
"We say no to the coronavirus bill. No to mandatory vaccines. No to the new normal and no the unlawful lockdown.
"Bring a picnic, some music and let's have some fun and say yes to life."
There are reports of similar events being planned elsewhere in the country too.
Councillor Ben Miskell, representative for Park and Arbourthorne ward, said: "Whether it will actually happen or not or if it's just to whip us all up into frustration and angst that people could be that stupid, who knows.
"The vast majority of people in Norfolk Park and across Sheffield are outraged when they see things like this.
"What we are dealing with at the moment is life and death and this isn't the time to be organising silly political protests against sensible measures to control a global pandemic."
One resident, Linda Wilkinson, commented on social media: "I can't believe I'm reading this. Have these people been asleep for the past two months? People are dying for God sake."
A spokesperson for South Yorkshire Police said: “We are aware of reports of planned gatherings at Endcliffe and Norfolk Park this weekend, as part of a series of events across the country.
“We would like to urge people not to attend these gatherings. Despite the slight easing of restrictions, the Government is clear that gatherings of three or more people who are not members of the same household remain against the law. It’s important people continue to adhere to these restrictions in order to stay safe and prevent the spread of Covid-19.
“We are closely monitoring plans in the lead up to the event and our officers will be patrolling the parks across the weekend. Our officers do have the power to disperse gatherings should they need to.”