During the match in Doha, Croatia fans verbally insulted Borjan, an ethnic Serb, who was born in Croatia but fled the country as a child.
They also brandished banners, including one which referred to a 1995 military operation that ended Croatia's independence war.
During and after the operation more than 200,000 ethnic Serbs fled the country, including Borjan's family.
A disciplinary inquiry fined the Croatian federation 50,000 Swiss francs (50,674 euros, $53,000) "in relation to the behaviour of Croatian supporters during the Croatia v. Canada FIFA World Cup match on 27 November", a statement announced.
Croatia's punishment comes 48 hours before they take on Brazil in the last-eight on Friday.
In other "footie fails," the Serbian federation were also in the FIFA dock, receiving a 20,000 Swiss franc fine over a controversial flag depicting Kosovo hung up in the team's dressing room during their group game against Brazil.
The Kosovo football federation (FFK) filed a complaint with the governing body after photos showed a version of the Serbian flag with a map including Kosovo as part of the country and stamped with the slogan "there will be no surrender".
Kosovo, a former Yugoslav province with an Albanian majority, declared independence from Serbia in 2008, which Belgrade refuses to recognize.
In a third case before FIFA's disciplinary committee six bookings for the Saudi Arabian team in their games against Argentina and Mexico cost their federation two fines of 15,000 Swiss francs each.