Alcoa has been purchasing its power from Hydro-Québec at a preferential rate, which is expected to rise by more than one cent per killowatt hour, or about 50 per cent overall.
The company said the increase would add 60 per cent to the cost of producing aluminum.
The company employs more than 3,000 workers at its aluminum smelters in Baie-Comeau, Deschambault and Bécancour.
This week, the company sent a letter to its unions stating that it was prepared to shut down three of its operations if Hydro-Québec insists on increasing its rate.
Premier Marois calls threats 'alarmist'
Premier Pauline Marois responded to Alcoa's plans on Wednesday and said she was surprised by Alcoa's reaction.
"I find their tone needlessly alarmist," she said.
Marois said high-ranking members of her government are in the process of negotiating with the company.
"It's a major industry that's very important for Quebec. It has been here for a long time, and it isn't going anywhere."