Mehmet Ali Talat, Turkish Cypriot leader, made the trophy presentation on the podium at Istanbul Park in a controversial move by organisers of the event.
Talat is the president of the separatist Turkish Republic of North Cyprus (TRNC), which is recognised only by Ankara, and the move to allow him to be at the grand prix in an official capacity outraged the internationally-recognised Greek Cypriot government which has no diplomatic relations with Turkey.
FIA ruled on Tuesday that the Turkish organisers had broken Formula One rules by politicising the event.
"The World Motor Sport Council has found against the National Sporting Authority of Turkey and the organisers of the Turkish Grand Prix on all counts," announced the FIA in a statement.
"The organisations have been fined a combined total of five million dollars."
Ethnic lines have divided Cyprus since 1974 after Turkey invaded the north of the island in response to a Greek Cypriot move to unite the island with Greece.
Turkish Cypriots declared the TRNC in 1983 with the Greek Cypriot government now extremely sensitive to any move that may support or recognise the breakaway state.
The general manager of the Cyprus Automobile Association said he was surprised at the leniency of the punishment, hinting that he expected more than just a monetary penalty.
"I'm surprised," Takis Kyriakides told state radio.
"It's a large amount but I would have expected much more than just a fine.
"We initially sent our protest letter explaining that he (Talat) was not president of a state and we let the matter takes its course before the FIA," added Kyriakides.
Ferrari's Felipe Massa won the Turkish Grand Prix - his first ever Formula One victory, five seconds ahead of Spaniard Fernando Alonso in his Renault, while seven-time world champion Michael Schumacher was third.