Naomie Tremblay-Trudeau told various media Friday she is considering legal action against the police after video of her being shot at point-blank range in Quebec City circulated on YouTube.
Camille Godbout of the ASSE student group says it wasn't an isolated incident.
She said a police dog attacked a protester earlier this week in Quebec City and that another demonstrator was injured after being allegedly struck by a police baton in Montreal.
The protests are aimed at getting the Couillard government to roll back austerity measures they say have affected the quality of public services in the province.
Godbout accused authorities of heavy-handed tactics and added it is time they adopted a different attitude.
"The authorities must rectify the situation and reconsider how they behave toward people who march in the streets to defend their ideals," said Godbout.
Public Security Minister Lise Theriault has asked for a report into Tremblay-Trudeau's case.
A spokesman for the Quebec City police says Thursday's incident will be investigated.
Francois Moisan said the protester was actually struck by a cardboard cap used to retain the gas and not the canister itself.
Moisan said police used the gas to keep protesters at bay.