At least one of the suspects in the attack by two gunmen was a student at nearby University Laval, the source said.
One suspect was identified as Alexander Bissonnette, a French-Canadian, the other as Mohamed Khadir, who is of Moroccan heritage although his nationality was not immediately known, according to the source.
Police declined to give details of the suspects' identities or possible motives for the attack during evening prayers at the Centre Cultural Islamique de Québec.
"Legal procedures are now underway and we cannot make any comment on the identity of the suspects," Royal Canadian Mounted Police national security superintendent Martin Plant told a news conference. He added the suspects, both men, were not previously known to police, Reuters reported.
One suspect was arrested at the mosque, where police were called at about 8 p.m. local time, and the other turned himself about an hour later, Quebec City Police Inspector Denis Turcotte said.
Police said they were confident there were no other suspects involved in the attack.
Canadian Prime Minister Justin Trudeau earlier called the shooting "a terrorist attack on Muslims."
The shooting came over the weekend that Trudeau said Canada would welcome refugees, after US President Donald Trump halted the US refugee program and temporarily barred citizens from seven Muslim-majority countries from entering the United States on national security grounds.
Trump's action was widely condemned in the United States and abroad as targeting Muslims.