Councillor Charlotte Atkins, leader of the Labour group on Staffordshire County Council, said pupils and parents had "suffered enough" already due to Covid-19.
She said children would return from their Easter holidays just a few weeks before they're out again due to people heading to the polls on May 6.
Councillor Atkins said: "School children have been off school for weeks with their parents making heroic efforts to home school them. This has been extremely tough for children who miss their friends, school routine and their interaction with teachers and other staff. Some parents are at breaking point trying to juggle work schedules or other caring responsibilities with the challenge of taking on their children’s learning and wellbeing.
"If schools are used as polling stations, they could be closed entirely, not just for one day, but longer to accommodate deep cleaning before and after voting takes place. It is vital that hard pressed council election teams do all they can to reduce the impact of these elections on schools. Otherwise, children will be back from their Easter holidays just a few weeks before they are out again for the elections.
"That break will be very unwelcome for children and parents who are desperate to get back to normal school timetables and to settle their children back into school life."
Elections will be held on May 6 – dubbed "Super Thursday" due to local council elections being held alongside police and crime commissioner and mayoral elections.
In the Black Country, voters will head to the polls to elect councillors to their local council, the West Midlands Mayor and the next police and crime commissioner (PCC).
Meanwhile, in Staffordshire, voters will head to the polls to elect councillors to Staffordshire County Council, Cannock Chase District Council, and Creswell Parish Council in Stafford.
Lichfield District Council, which has an election every four years and last held one in 2019 like Stafford Borough Council, will hold a by-election in the Summerfield and All Saints ward for a district councillor. Voters will also be electing the Staffordshire Police, Fire and Crime Commissioner.
Councillor Atkins added: "The search for alternative polling station sites is urgent to avoid this further disruption of schools. Children and parents have suffered enough already."
"I also urge all electors to make things easier for themselves by applying immediately for a postal vote so they can vote safely and early from home. Then whatever happens everyone can exercise their democratic right on May 6."