'I am not concerned about trouble in 2018, I have full confidence in the Russian authorities,' Infantino said on the sidelines of a meeting in Doha, Qatar.
The comments came ahead of the broadcast of a television documentary in Britain on February 16 in which hard-line Russian fans are said to have threatened English fans who attend the World Cup.
Russian and English fans clashed at the Euro 2016 tournament in France and several Russians were expelled.
Infantino also said he has not asked Russian Deputy Prime Minister Vitaly Mutko to resign as chief organizer of the 2018 World Cup.
Mutko has faced questions about his role as head of the Russian World Cup organizing committee after being linked to large-scale doping by Russian athletes.
Mutko has denied any knowledge of the doping that a report by a World Anti-Doping Agency investigator said was 'state-sponsored.'
Mutko is seeking a new place on the FIFA council in a vote in April and must pass an integrity check.
On a separate topic, Infantino said he intends to encourage co-hosting for the 2026 World Cup that could divide the tournament up between as many as four countries.
The only time FIFA has previously approved co-hosting was in 2002 when Japan and South Korea staged the tournament.
Based on reporting by AFP and Reuters