Both the Croatian and Turkish federations already face charges in the aftermath of the match between the two sides on 12 June.
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The official bent down to pick up a flare thrown onto the pitch – but it went off inches from his face.
The fan was then led away.
UEFA later confirmed a disciplinary case would be opened on Saturday.
“I hope these people are identified and punished”, Cacic said.
For the most part of the encounter between Croatia and Czech Republic, it looked the Croats would be heading for a comfortable win.
Asked if he had any news about his club future, Vardy said: “No, nothing at all”.
“It was a very hard moment for me and my family”.
Croatia had stuck first during the match when Ivan Perisic scored in the first half. “This is probably the most important match in the group stage for us”.
Croatia’s president Kolinda Grabar-Kitarovic slammed the violent fans as “enemies of Croatia”.
“We will not be stopped by these hooligans and we will not let them shatter our dreams”, said Cacic.
Earlier last week, French riot police sprayed tear gas and charged England fans in Lille before the England vs Wales match.
Belgium coach Marc Wilmots has made three changes, including dropping Radja Nainggolan and Marouane Fellaini to the bench.
Meanwhile, the Russian government maintained its offensive over the treatment of its fans in France.
“The majority of the fans are telling them to not do it”.
Hungary supporters light a flare on the stands during the Euro 2016 Group F soccer match between Iceland and Hungary at the Velodrome stadium in Marseille, France, Saturday, June 18, 2016.
Croatia has a track record of disruptive fans at the European Championship.
Uefa has brought charges for the setting off of fireworks, the throwing of objects, crowd disturbance and racist behaviour by Croatia fans in Saint-Etienne.
“The Saint-Etienne incident is the product of the passivity of the Croatian state, and today we have all become hostages of a group of hooligans”, the Croatian federation said in a statement.
The actions of Croatia’s fans had a bad impact on their team, with Czech Republic – who had been trailing 2-0 – roaring back with two late goals to nick a draw.
Barcelona midfielder Ivan Rakitic fears they will be thrown out of Euro 2016 after crowd trouble.
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Croatia’s fans have built up a track record of trouble in recent years.
