A group of around 200 Hungary fans broke through flimsy segregation before their 1-1 draw with Iceland at the Stade Velodrome, charging from one end of the stadium to another and clashing with stewards.
Flares and firecrackers were also lit after Birkir Saeversson's 88th-minute own-goal, which left Hungary top of Group F with one game to play.
UEFA are looking into the "setting off of fireworks", "throwing of objects" and "crowd disturbances" by Hungarian supporters.
The Russian Football Union were given a €150,000 fine and a suspended disqualification from the tournament after the incident - which followed a day of fighting between Russian fans, their English counterparts, local gangs and police.
UEFA will rule on a suitable punishment for Hungary on Tuesday.
Fireworks set off by Belgium fans during their 3-0 win over Republic of Ireland could also land their federation in trouble, while Portugal's authorities have questions to answer after a fan came on to the pitch after their 0-0 draw with Austria at the Parc des Princes to take a photo with Cristiano Ronaldo.