They could face sanctions due to fans "throwing objects and setting off fireworks" during Friday's matches and a hearing into the unrest will take place on Monday, UEFA -- European football's governing body -- said in a statement.
Croatia faces additional charges over alleged "racist behaviour", while Turkey faces charges linked to a pitch invasion by supporters.
The incidents took place when Turkey played Spain in Nice and during Croatia's clash with the Czech Republic in Saint-Etienne, the latest crowd trouble to hit the tournament.
Friday's match in Saint-Etienne was held up for several minutes after Croatian fans threw flares onto the pitch and began fighting among themselves.
Eight flares and other objects landed on the pitch near to riot police, who had been deployed in front of the section housing Croatia's supporters.
The trouble broke out in the dying minutes of a game that Croatia were leading 2-1. The final score was 2-2.
Croatia, sanctioned three times during the qualifying competition, was already facing a disciplinary hearing on Tuesday after fans threw flares and ran onto the pitch during the team's opening match at the finals against Turkey in Paris.
"ULTRAS"
A police official told Reuters on Saturday 11 hardcore fans known as "ultras" -- some of them carrying neo-Nazi banners -- had been detained in Nice before Friday's Spain vs Turkey match.
Philippe Castanet, a deputy prefect for the region, said some of them would be sent home.
Inside the stadium, five fans were arrested for the possession and throwing of flares.
Police moved in at the Stade Velodrome in Marseille on Saturday ahead of a game between Iceland v Hungary.
"Supporters tried to climb a fence but there was no violence," a spokesman for regional police said.
Supporters in the stands were seen by a Reuters witness making what looked liked a Nazi salute.
Euro 2016 has been marred by violence, especially in Marseille last weekend when Russian fans clashed with English supporters before, during and after the Russia vs England game.
On Saturday, a Reuters witness saw dozens of Russian fans leave a Marseille detention centre under police escort. Shortly afterward, another witness saw them arrive at Nice's international airport.
In Lyon, two Ukrainian fans were filmed on Thursday during the Ukraine vs Northern Ireland game with tattoos similar to the swastika. The region's prefect said he had contacted a judge about the matter.
Earlier this week, French riot police sprayed tear gas and charged England fans in Lille before the England vs Wales match.
France has enlisted more than 90,000 police, soldiers and private security agents nationwide to ensure safety in the face of intelligence agency warnings of potential militant Islamist attacks and the threat of hooliganism.
(Additional reporting by Mathias Galante, Catherine Lagrange; Writing by Matthias Blamont and Julien Pretot; Editing by Gareth Jones and Helen Popper)
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