The announcement was made early Wednesday, but the union local did not release the results of the vote.
The 23,000 inside workers include child care workers, ambulance dispatchers, nurses, janitors and parks and recreation staff.
They can strike or be legally locked out on Saturday, which means daycares, most recreation centres and city-run swimming pools would be closed.
However, the union says it has no intention of walking off the job Saturday, even with a strike mandate.
Local 79 president Tim Maguire says the union is "prepared to keep bargaining beyond the arbitrary deadline imposed by the city."
"We are going to consider the option this mandate gives us if the employer starts to gut our collective agreement and strip away basic rights and protections," he said.
Maguire said the strong strike mandate will assist the union in reaching a fair settlement, as well as uphold basic employment protections for the workers.
The union has accused the city of bargaining in bad faith and filed a complaint with the Ontario Labour Relations Board.
But the city says the union has been unavailable for negotiating for seven of the last 17 days.
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