The 25-year-old reported himself to police on Saturday afternoon, less than 24 hours after the incident in the Euro 2016 qualifier.
The Montenegrin interior ministry said the fan was suspected of throwing the flare from the north stand during the clash.
The fan was identified on video footage.
"L.L [the fan] is suspected of throwing a flare during the match between Montenegro and Russia from the north stand at the City Stadium in Podgorica, hitting the Russian goalkeeper in the back of the neck," the ministry said in a statement.
Three people suspected of using flares have been identified, while two others have been arrested for incidents before and after the game.
The clash was marred by multiple incidents before being called off in the 67th minute, when Dmitri Kombarov was hit by a missile thrown from the stands.
UEFA is awaiting reports from the match.
