The match was abandoned in the second half after a brawl involving players and staff, with Russia's Igor Akinfeev having earlier been struck by a flare.
The Montenegrin FA (FSCG) has been charged with holding a match that was not played in full, while both the FSCG and Football Union of Russia have been charged with the throwing of fireworks and other missiles by fans.
Russia have lodged a formal complaint with Uefa, demanding they be awarded victory from a match that was 0-0 when it was abandoned by German referee Deniz Aytekin.
Goalkeeper Akinfeev was stuck on the head by a flare in the first minute of the Group G clash at the Gradski Stadion, leaving the field on a stretcher.
He was taken to hospital in the Montenegrin capital with a neck injury and minor burns, but was discharged after an examination determined he had no major injuries.
Following a delay of more than 30 minutes, the match restarted but it was abandoned on 67 minutes when fighting broke out after Russia midfielder Roman Shirokov's penalty was saved and team-mate Dmitri Kombarov was struck by a missile.
Russia and Montenegro, who included Manchester City striker Stevan Jovetic in their starting line-up, are tied on five points in the group.
Uefa has charged the Montenegrin and Russian football associations following the abandonment of Friday's Euro 2016 qualifier in Podgorica.