The cost-saving measure is part of the cash-strapped council's three-year medium term saving-plan, which seeks to claw back money following central government cuts.
But opposition leaders have aired uncertainties regarding the proposal.
They believe the measure should be optional – and not compulsory – because it could hit staff on lower wages the hardest.
Councillor Les Jones, Chairman of Dudley Council's Corporate Scrutiny Committee, said: "There are a number of options available to the council including this measure.
"At the moment it is just a proposal and it will be subject to negotiations such as with trade unions.
"The current proposal from the council is that this would be compulsory, but some people will not be able to afford it.
"Our view is that would be overkill, and it would be disproportionately unfair on people who could not afford to take unpaid holidays."
Councillor Jones said that he would agree to the cost-saving measure if it was made optional to staff
He felt that the proposal would be suited to some sections of staff more than others.
"It could be suited to those in senior management," he said. "But not those that work in adult social care because 24/7 care is needed."
Councillor Pete Lowe, leader of the council, said: "The proposal includes unpaid leave over Christmas and Easter which means the council will shut down over the quieter holiday periods, although essential and emergency services will continue to run.
"We will now embark on really meaningful discussions with the trade unions."
The proposal would also mean petrol allowances for staff would drop from 55p to 45p to cut costs.
Dudley Council is currently making a raft of savings following government cuts.