It said a report it commissioned, completed by independent engineers, shows mistakes made by the firms led to the collapse of concrete grids onto the Ville-Marie Expressway below.
A concrete grid serving as a sun shield detached from the tunnel ceiling on Sunday, July 31, near the city hall exit.
It was a weekend morning and the tunnel was virtually empty when the 25-tonne concrete slab crashed on road.
Transport Minister Pierre Moreau said a hydro-demolition procedure, which removes old, flaking concrete from the tunnel walls, caused the collapse.
"It jeopardized the structure," said Moreau.
The provincial government now wants the engineering firms CIMA+, Dessau and SNC-Lavalin and construction company Laco Construction, to cover the costs that followed the collapse.
Moreau said it cost almost $3.5 million to pay workers to clean the area and to ensure the structure was safe after the collapse.
The government said it would consider taking the firms to court if the money isn't handed over.
The firms involved in the tunnel repairs told the CBC they would not comment on this issue while lawyers examine the demand.