A 47-year-old man was arrested after the altercation on Saturday outside the Centre culturel islamique de Québec.
Police told Radio-Canada that the suspect walked into the mosque's parking lot, where he began speaking to at least two people near the mosque's entrance.
As the exchange escalated, the suspect assaulted a man outside the mosque, said police spokesperson Sandra Dion.
Mosque president Mohamed Labidi said the suspect in Saturday's incident was saying hateful things to those outside the mosque.
"He was insulting Muslims. We have a witness, we have videos, we have everything," Labidi told Radio-Canada.
Quebec Premier François Legault said what happened outside the mosque was "unacceptable."
Éric Caire, the MNA for La Peltrie, where the Quebec City mosque is located, said "the Muslim community is being targeted."
"What's important for me is that the police officers give all the necessary protection to the Muslim community," he said.
In a statement, the National Council of Canadian Muslims (NCCM) executive director Mustafa Farooq said he was saddened to hear of the incident, but was not shocked.
Quebec Public Security Minister Geneviève Guilbault said she would not ask for increased security around the mosque as police continue to investigate the incident.
She said police are already paying special attention to the mosque, given the repeated incidents there.
The mosque was the site of the Jan. 29, 2017, shooting where gunman Alexandre Bissonnette opened fire after evening prayers, killing six people and seriously injuring several others.
About six months before the shooting, a pig's head was left outside the mosque during Ramadan with the message "bon appétit."
In July 2017, a defaced Qur'an was mailed to the mosque around the same time as residents in nearby Saint-Apollinaire, Que., held a referendum over the construction of a Muslim cemetery. Residents voted against constructing that cemetery, 19-16.
The head of the NCCM said that the CAQ's secularism bill, which would ban state employees including teachers, prosecutors and police officers from wearing religious symbols, adds to the "divisive" atmosphere in the province.
Immigration, Diversity and Inclusion Minister Simon Jolin-Barrette, the author of the bill, disagreed. While condemning Saturday's assault, he said that no one religion is targeted by the bill.
He pointed to his denunciations of a retired senator linking the hijab to female genital mutilation and the mayor of Hampstead calling Bill 21 "ethnic cleansing" as examples of how he is moderating the debate over the bill.
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Police say a 47-year-old man has been arrested after an altercation outside Quebec Citys largest mosque.
Quebec City police say a skirmish broke out between a man and some taxi drivers in the parking lot of the Centre culturel islamique de Quebec shortly after noon on Saturday.
The Canadian Press was unable to reach the mosques president, but the National Council of Canadian Muslims said on Twitter that the suspect had expressed hostility towards Muslims and immigrants prior to the altercation.
The mosque is the site of a 2017 shooting that left six men dead and several injured after a gunman stormed the building and opened fire.