Vida scored an extra-time goal and one of Croatia's penalties in a 4-3 shootout win over the World Cup hosts in Sochi on Saturday.
Croatia will play England in the semi-final on Wednesday and some Russian officials had called on football governing body FIFA to take tough disciplinary measures.
The ponytailed 29-year-old shouted "Glory to Ukraine!" in a video posted by former Croatia international Ognjen Vukojevic shortly after the dramatic finale in Sochi.
Vida used to play for Ukrainian club Dynamo Kiev. Vukojevic also played for the club and now works for them as a scout.
FIFA said it had studied the video and decided to issue a warning to Vida but not take any further measures.
"We can confirm that FIFA's disciplinary committee has sent a warning to the player Domagoj Vida due to his video statement," a spokesman told AFP.
"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 (Kiev) 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."
Vida issued a statement distributed by Croatia's football federation after the FIFA ruling calling the entire incident a misunderstanding.
"I regret that some media representatives have interpreted our communication in such a manner," he said.
"It was definitely no political message, but a simple thank you for all the support from Ukraine, where Vukojevic and I spent a number of years."
He had earlier told Russian media that the message was "just a joke".
Croatia's football federation added that the players' message was "intended for their friends in Ukraine".
"Nonetheless, the Croatian football federation has pointed out to both Vida and Vukojevic, as well as all other internationals, to refrain from any messages that could be politically interpreted in the future," it said.