However, Croatia avoided a stadium closure, which football's governing body has ordered for World Cup qualifiers in other discrimination cases this season.
The latest case involving Croatia fans follows criticism from UEFA President Michel Platini last June after a series of incidents at the European Championship, including racial abuse targeted at Italy forward Mario Balotelli.
FIFA acted on eyewitness reports from discrimination monitor Fare at the March 22 match in Zagreb between two former Yugoslavia republics which fought a war in the 1990s.
Fare identified "at least seven different nationalist songs seen in the context of the Balkans as likely to cause hatred and lead to discriminatory acts."
"Croatian supporters in different ends of the stadium repeated in turns the sentence 'In fight for homeland!'" reported Fare, a European network of fan groups.
Visiting fans were barred for security reasons from the match, which Croatia won 2-0.
The Croatian FA can appeal the sanction, which was applied this month as FIFA and UEFA prepare to introduce tougher sanctions for racism and discrimination.
On Friday in Mauritius, FIFA's 209 member countries will consider approving formal measures at their annual meeting.
Croatia, which hosts Scotland at Maksimir Stadium in Zagreb next week, avoided a closed-door order which FIFA imposed on Bulgaria and Hungary at matches in March following racist abuse incidents.
Tense relations between Croatia and Serbia meant it was previously decided that to tickets will be sold to away fans for the countries' return match in Belgrade on Sept. 6.
Croatia leads a six-team qualifying group along with Belgium, nine points clear of third-place Serbia.Suggest a correction