Dick Advocaat's side's comprehensive 4-1 victory was marred by allegations of racism and violence both during and after the game in Wroclaw.
During the game, there were reports from Football Against Racism in Europe (FARE) that Czech defender Theodor Gebre Selassie was subject to racist chanting, while there were also allegations that fireworks were thrown and offensive banners were displayed in the crowd.
FARE chief executive Piara Powar told Press Association Sport: "Our observer reported descriptions of that nature. It was directed at the Czech Republic's only black player."
And, following the game, images were released showing Russian fans attacking stewards in a walkway at the stadium, something that Uefa has confirmed will also be investigated.
Michal Zachodny, Goal.com correspondent who was at the Russia-Czech Republic game in Wroclaw on Friday night, reports: "The feeling among other journalists I talked with after the game was that everything had passed okay, except for two flares that went off among Russian fans.
"Today, it was revealed that there was a fight in one pub between Russian and Czech supporters but they were quickly separated by police. As for the fight inside the stadium after the game, it is now known that police have pictures of those who attacked stewards and are cooperating with Russian police to identify and locate them before the game with Poland on Tuesday."
Michal adds: "There is already talk that Russian fans will march before Tuesday's game against Poland with much-hated signs - communists signs, USSR flags - and do as much as possible to annoy Polish fans hooligans who, given their nationalism, are much against this march."
Uefa’s Control and Disciplinary Body will review the case on Wednesday 13 June.