Reports say the man was shot and remains in critical condition.
Local police were at the scene at 8 p.m. ET on Friday night and were later joined by the provincial police because the suspect was known to be armed.
Gunshots were heard at the scene on Père-Frédéric Street in Trois-Rivières, about 150 kilometres west of Quebec city, around 11:30 a.m. ET. on Saturday.
Radio-Canada reports that neighbours were asked to stay inside and away from windows to keep safe from possible stray bullets.
Police were allegedly looking to arrest the man after being called to the scene of an altercation between the suspect and another man.
Quebec City police will be investigating the matter since both the Trois-Rivières police and the Sûreté du Québec were involved in the situation.