An FIA statement said that 'The worker was helping to recover a car which had stopped during the race. The recovery vehicle had lifted the car to return it to the pits and while doing this the worker dropped his radio and attempted to pick it up. As he did this, he stumbled and was hit and run over by the recovery vehicle.'
The unidentified man was transported by helicopter to Sacre-Coeur Hospital, but he later succumbed to his injuries.
The fatality is the first at a Formula 1 event since 2001.
Several drivers have expressed their condolences.
"Today there is nothing to celebrate. Terrible news arrives with the death of a marshal this race. Very sad. RIP," said Fernando Alonso.
"It is very, very sad to hear that a marshal tragically lost his life today in Canada," said race winner Sebastian Vettel.
"The work of marshals is not always seen but it is vital to our sport and without their commitment, time and dedication there would be no motorsport. I am very, very sad to hear this news and my thoughts are with his family and friends," he continued.
Esteban Gutierrez, whose stricken car was involved in the incident, added 'My dearest condolences to the family of the marshal who lost his life today, our prayers for him and his family. RIP.'