Montreal police confirmed the family link between Galarneau and all three victims, but did not confirm the respective relationships.
Authorities say the suspect had no prior criminal record.
The arrest of the 19-year-old, who was covered in blood, outside the apartment building on Bélanger Street was filmed by witnesses and broadcast on social networks.
The incident happened shortly after 9 a.m. Friday when police were called to the residence and found three bodies with multiple stab wounds. All three victims were pronounced dead at the scene.
The crime scene was subject to a security perimeter. Several police vehicles were on-site and a command post was established. Neighbors were also interviewed.
At a press conference later that day, Premier François Legault called the event a "really troubling" situation.
Asked about the number of fatal domestic violence incidents in recent weeks, Legault said there were mental-health issues everywhere in the world and that his government would "continue its support," reiterating an increase in funding to mental-health resources in the province's annual budget which will be presented next week.
The suspect will return to court on April 11 for further proceedings.