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.

The Magpies have lost five league games in a row and are only four points above the relegation zone.
Crossley told BBC Radio Nottingham: "If Notts County were without a manager and looking for someone to get them out of it, John would be an automatic choice."
Sheridan, 52, and Crossley, 47, joined Notts prior to the start of the season.
"I know the chairman is really eager for us to do well," added former Nottingham Forest keeper Crossley.
"He has been brilliant with and he still thinks we are the right people to turn it around. We can ask no more from him. He is with us and by us.
"But we're realistic. We have lost five on the bounce and this is a results-based industry.
"We know what we have to do and as far as we are concerned we will do it. But we need more from the players."
Crossley said the club had "targets" and were looking to bring in players in the January transfer window as they look to get through a "sticky period".
"Things have to change. We realise that and they will change in January," he said.
"There is only way to get through this and that is by everyone working hard every single day and eventually it will turn."
Uefa has charged the Montenegrin and Russian football associations following the abandonment of Friday's Euro 2016 qualifier in Podgorica.
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Assistant manager Mark Crossley says boss John Sheridan has the backing of chairman Ray Trew, despite Notts County slipping to 20th place in League Two.