Ivan Kuliak wore a tank top with the symbol "Z" on his chest when he received his medal during a World Cup competition in Doha in March.
Next to him stood the Ukrainian gold medalist Illia Kovtun.
The letter was seen on Russian vehicles during the war in Ukraine and has become a symbol of the invasion.
The Gymnastics Ethics Committee, GEF, has now decided to suspend Kuliak for one year because it is believed that he has violated the rules of the International Federation, FIG.
"Mr. Kuliak may not participate in events organized by FIG and may not participate in competitions organized by any of its affiliates for one year from the date of this decision (May 17)," writes GEF.
Kuliak must also return his bronze medal from the World Cup competition and the prize money of the equivalent of 5,000 kronor.
Kuliak has 21 days to appeal the decision.
Since the incident, all Russian and Belarusian gymnasts have been expelled from international competitions, but Kuliak will have to wait longer than his compatriots to compete internationally.
"If the safeguard measures that prevent Russian and Belarusian athletes from competing still stand on May 17, 2023, the suspension will continue and expire six months after the said measures are removed," writes GEF.