The names will be presented to leader Julie Dore at a full council meeting next Wednesday, July 3.
Protesters will also gather outside the Town Hall at 1pm before the meeting to hear speeches and raise a Palestinian flag.
Julie Pearn, chair of Sheffield Labour Friends of Palestine, said: “The size of the petition is unprecedented and demonstrates the wish of ordinary citizens to see justice for Palestinians, who have suffered dispossession of their homes, Israeli military occupation, human rights abuse and siege over the decades since 1948.
“While largely symbolic, Sheffield’s recognition of the Palestinian right to statehood would be significant. The UK government has always taken a timid approach under United States pressure but many feel that the tide of public opinion is turning.
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“Sheffield would be the first UK council to take this step and set a precedent, just as happened with its recognition of Somaliland as an independent state, which other councils followed.
“Sheffield has a strong tradition of supporting international campaigns for justice, such as the anti-apartheid movement.”
Palestine and Israel have been in conflict for decades, with both laying claim to the same territory. Palestine is not recognised as a state by Israel – but, of last year, 137 United Nations members disagreed with this stance.
Jeremy Corbyn, Labour’s national leader, has pledged to recognise Palestine as a state if the party is elected into power.
Neville Wright, who supported the petition, commented: “Though many of us in Sheffield are currently finding life difficult, much of what we take for granted is a never ending struggle for our Palestinian brothers and sisters.
“Such a small gesture as recognition of the State of Palestine is such a shot in the arm for those facing daily hardship. Sheffield Council does not have to wait for a Labour government, be bold and make this statement now.”
The petition will be presented at a full council meeting on Wednesday, July 3 which starts at 2pm.