Hossa was born in Stará Ľubovňa, Czechoslovakia, to František Hossa, who was a professional hockey player, and Mária Hossová, a clothing designer. Hossa's brother who is two years younger than him, Marcel Hossa, was drafted by the Montreal Canadiens 16th overall in the first round in the 2000 NHL draft. Following in his footsteps playing for both of Marián's previous junior teams, Dukla Trenčín and the Portland Winter Hawks. Both of the Hossa's have played together for Mora IK of the Elitserien during the 2004–05 NHL lockout and on the Slovak national team in the World Championships and Winter Olympics. Coincidentally, they were both dealt by their NHL teams on the day of the 2007–08 trade deadline — Marián from Atlanta to Pittsburgh and Marcel from the New York Rangers to the Phoenix Coyotes. The younger Hossa is no longer playing professional hockey. His last season was in 2017–18, where he played with HK Dukla Trencin. Hossa also grew up with Marián Gáborík and Zdeno Chára in Trenčín, and remained close friends with them through his NHL career. Trenčín honored the trio by naming three streets after each skater in 2015. Marián's father was head coach of the Slovak national team and coached his sons in several tournaments.