Internationally, Gavrikov won an Olympic gold medal with the Olympic Athletes of Russia in 2018, where he posted three points (2-1=3) in six tournament games. He has also appeared in six IIHF tournaments, including four IIHF Men's World Championships (2021, 2019 - bronze, 2018, 2017 - bronze), one IIHF World Junior Championship (2015 - silver) and one IIHF Under-18 Men's World Championship (2013). At the 2015 IIHF World Junior Championship, Gavrikov was tabbed the tournament's best defenseman after guiding Russia to a silver-medal finish.