The 20-year-old wore a 'Z' symbol taped to his leotard while standing next to Ukrainian gymnast Illia Kovtun on a podium in March -- Kovtun won gold and Kuliak picked up bronze in the parallel bars at the gymnastics World Cup event in Doha, Qatar.
The 'Z' insignia has been displayed on tanks and vehicles used by the Russian military and has become a symbol of support for the invasion of Ukraine.
The International Gymnastics Federation (FIG) criticized Kuliak for his "shocking behavior" and the athlete has now been sanctioned by the Disciplinary Commission of the Gymnastics Ethics Foundation (GEF) for violating FIG rules.
The GEF ruled that Kuliak is banned from any FIG affiliated event for 12 months and must return his bronze medal.
"If the protective measures keeping Russian athletes from competing are still in place on 17 May 2023, the ban shall continue and expire six months after the removal of said measures," the statement added.
Russian and Belarusian athletes and officials, including judges, are not allowed to take part in official FIG-sanctioned competitions following advice from the International Olympic Committee amid the invasion.
Kuliak must also repay the prize money of $501.77 and pay $2,007 towards the cost of proceedings.
The gymnast has 21 days to appeal the decision.
CNN has reached out to the Artistic Gymnastics Federation of Russia (FSGR) regarding any possible appeal but has not received a response.
Amid criticism, Kuliak said he would "do exactly the same" if given another chance, according to Russian state media at the time.
"I saw it with our military and looked at what this symbol means. It turned out [it means], 'for victory' and 'for peace,'" Kuliak is quoted as saying in Russia-controlled media outlet Russia Today.
"I didn't wish anything bad on anyone, I just showed my position. As an athlete, I will always fight for victory and stand for peace."