Grabar-Kitarovic flew in from Zagreb on a charter flight organised for Croatian soccer fans planning to attend the match, which is due to start at 1800 GMT on Saturday.
Veniamin Kondratyev, head of Russia's southern Krasnodar region, met the Croatian President at Sochi's airport, his administration said in a statement, adding that 10,000 Croatian fans were expected to attend the game.
"A crucial match is ahead of us, I am sure both teams will perform well and show us a beautiful game," Kondratyev was quoted as saying by his administration.
Russia's TASS news agency quoted fans who took the same flight as Grabar-Kitarovic as saying that some of them took selfies with the president during the flight.
"She likes the sport, and what she is doing now is normal for the president. She took a flight with ordinary people, greeted everyone. And I like it: we have a small country, we are like one team," one of the Croatian fans told TASS.
Russian Prime Minister Dmitry Medvedev is expected to attend the match with Grabar-Kitarovic, TASS said.
(Reporting by Polina Devitt; editing by Andrew Osborn)
