UEFA said it would launch an inquiry after the second outbreak of stadium unrest in a week at the showcase tournament. Twenty Russian fans are to be expelled on Saturday.
At least eight flares thrown from the Croatian section of supporters in the Saint Etienne stadium landed on the pitch in the 86th minute. One steward appeared to be hit by one of the flares.
Croatia were leading 2-1 when English referee Mark Clattenburg halted proceedings so the flares could be extinguished.
Captain Dajijo Srna ran to the Croatia corner of the stadium to appeal for calm. But punches were then thrown between fans and stewards cleared the section.
When the game resumed, Czech Republic scored an equalising goal to finish 2-2.
Croatia got into trouble with UEFA last year after a Nazi swastika symbol was drawn on a pitch before a Euro qualifier against Italy.
The country's coach Ante Cacic said Croatian fans are "really scary".
"I hope these people are identified and punished," said Cacic. "These people are really scary, that is why I call them hooligans. These are not fans, these are sports terrorists."
- Sanctions loom -
A UEFA spokesman said an official inquiry would be launched on Saturday. Croatia already face punishment over a firework thrown on the pitch and a fan who got on to celebrate during the country's first Group D game against Turkey.
Croatia's fans have a history of trouble.
UEFA ordered the country to play two Euro qualifying matches behind closed doors, deducted a point and fined the federation 100,000 euros over the swastika incident last year.
European football's governing body also barred Croatia from playing qualifiers in the city of Split, which hosted the 1-1 draw with Italy on June 12.
In November 2014, Croatia's qualifying match in Italy was halted for 10 minutes because flares were thrown on the pitch leaving the Milan San Siro stadium engulfed in smoke. UEFA then ordered Croatia to close an 8,000 section of their ground for their next game and fined the federation 100,000 euros.
Croatia's star player Luka Modric, at the time called the fans' behaviour "madness".
It was second major episode of stadium turmoil at Euro 2016 after Russian fans attacked English counterparts after their game in Marseille last Saturday.
UEFA threatened to disqualify Russia if their fans cause more disturbances in a stadium. Their fans, who also clashed with England fans in Marseille city centre, were found guilty of crowd disturbances, racist chants and throwing firecrackers.
A court in Marseille on Thursday jailed three Russian fans for up to two years for their role in the street violence.
Twenty other fans are to be expelled on Saturday on a flight from Nice to Moscow.
Thirty-five people were injured, two England fans seriously, in the street battles. French prosecutors say they will launch an attempted murder inquiry.
The fan troubles have even caused a diplomatic incident between Russia and tournament hosts France.
The French ambassador was called in for a protest by Russia's foreign ministry, while President Vladimir Putin waded into the debate on Friday saying: "I truly don't understand how 200 of our fans could beat up several thousand English."
A French court on Friday ordered three Nice fans accused of attacking Northern Ireland supporters to be held in jail while they await trial in case they cause more trouble during Euro 2016.
A fourth Nice 'ultra' was released on bail ahead of the July 13 trial while prosecutors have not yet charged a fifth suspect who suffered a serious head injury in the street battle on June 11.
The brawl erupted outside an Irish pub in Nice where several hundred Northern Ireland fans had gathered ahead of their match against Poland the next day. Nine people were injured in the intense three minute battle in which bottles, glasses and other objects were thrown.