Modric, who joined Real Madrid from Tottenham Hotspur in 2012 for a reported 40 million euros ($45.40 million), was criticised in his debut season at the Bernabeu and named the worst signing of the year in a poll by newspaper Marca.
Hegerberg is a three-time Women's Champions League victor with French side Lyon and scored a tournament-record 15 times last season.
And asked whether he'd rather have won the World Cup or the Ballon d'Or, Griezmann insisted: 'The World Cup!'
'I won the Europa League, I won the Super Cup and the World Cup so it's a great year.
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Hegerberg, a three-time Women's Champions League victor with Lyon, was selected by a jury of 45 journalists as the cream of the crop in female football.
Hegerberg refused and quickly left the stage. "Being a women's footballer and winning the Ballon d'Or tonight is a step for me to take that action, personally". Brazil star Neymar was third past year but only 12th this time. "I used to play more offensively", said the Croatian.
When describing his feelings on winning the award, Modric added: "It is hard to express my emotion and how I feel in words". Kylian Mbappe, Lionel Messi and Salah held the fourth, fifth and sixth place respectively.
Modric, 33, was announced as the victor of the prestigious prize at a glitzy ceremony at Paris Grand Palais ahead of Ronaldo and French World Cup victor Antoine Griezmann.
The Portuguese - who wasn't in attendance at the event - has won the previous two iterations, but missed out to former Real Madrid teammate Luka Modric.
France Football, which hands out the Ballon d'Or, and FIFA combined their awards to create the FIFA Ballon d'Or in 2010. France coach Didier Deschamps said a French player should have won the award.