He is accused of having shot him in the leg.
Georgian police have arrested Merab Beselia, vice-president of the National Rugby Federation, Reuters reported on Thursday.
The latter is suspected of having opened fire on Wednesday on Ramaz Kharazishvili, former captain of the Georgia Sevens rugby team, on the premises of the federation.
The 32-year-old was immediately hospitalized for surgery.
According to a hospital source, his life is not in danger.
Georgian police investigation
Local media claim that an argument between the two men is the cause of the shooting.
Police have launched an investigation into the illegal buying, possession and carrying of a weapon and injuries.
Rugby is one of the most popular sports in this former Soviet republic.
The national rugby XV team, nicknamed the Lelos, has participated in all the World Cups since 2003. In November and December, it will play the Autumns Nations Cup, a new competition where it will face England, Wales and Ireland.