FIFA did not give any details of the chanting but said it had received a report from observers at the match at the Luzhniki Stadium which Croatia won 2-1 after extra time.
"We can confirm that a report has been filed through the anti-discrimination monitoring system in relation to chants of a possible discriminatory nature by English fans at yesterday's match," FIFA said in a statement on Thursday.
"Subsequently, disciplinary proceedings have been opened against the Football Association... As proceedings are ongoing, please understand we cannot comment further at this stage."
FIFA has employed teams of specialist observers at all World Cup matches to detect possible racist and homophobic chanting and banners at matches.
(Writing by Brian Homewood; Editing by Christian Radnedge)
