FIFA, world football’s governing body, said it was investigating.
“FIFA is processing the different reports of the said match as well as potential evidence concerning the matter referred to in your message,” a FIFA spokesperson told AFP.
“Until we have evaluated all information available, we cannot comment further.”
Vida later told Russian media that he meant no offence.
“It love Russian people,” Vida was quoted as saying. “It was just a joke.”
“Glory to Ukraine!” was a slogan of the former Soviet republic’s pro-EU revolution that toppled a Russian-backed president in 2014.
The revolt was condemned as illegal by Moscow and sparked a crisis in relations between the two neighbouring states.
It was followed by Russia’s annexation of Ukraine’s Crimea peninsula and a pro-Kremlin separatist war in eastern Ukraine that has claimed more than 10,000 lives.
Vukojevic added in the video: “This victory is for Dynamo (Kyiv) and for Ukraine! Croatia onwards!”
The clip was picked up by Russian state media and drew condemnation from some officials.
“Such actions should be punished,” parliament’s sports committee member Dmitry Svishchyov told the RIA Novosti state news agency.
“Political, nationalist and racist slogans are not welcome at the World Cup.”