Newly signed Real Madrid goalkeeper Thibaut Courtois won the best goalkeeper's award - beating Kasper Schmeichel and Hugo Lloris in the process. "Hopefully we can be the same for next generations", said Modric.
The 32-year-old Marta, whose Orlando Pride team reached the U.S. National Women's Soccer League (NWSL) playoff semi-finals, had won the previous FIFA Women's Player of the Year award five times, most recently in 2010.
For a sixth straight season, Ronaldo was the Champions League´s top scorer with 15 goals and also scored four times at the World Cup, including a hat-trick against Spain in a thrilling 3-3 draw to open Portugal´s campaign.
Messi and Ronaldo were not in attendance to be recognised as they opted to skip Monday's ceremony at London's Royal Festival Hall.
Portugal worldwide Ronaldo, who joined Juventus from Real Madrid in the close season, was second in this year's awards with Liverpool's Mohamed Salah in third place.
The Egyptian was also not included in the FIFPro World XI, with the likes of Ronaldo, Kylian Mbappe, Eden Hazard and Lionel Messi being named to the squad instead.
France's World Cup-winning boss Didier Deschamps claimed the coach of the year title ahead of Croatia's Zlatko Dalic and Zinedine Zidane, formerly of Real. "In life you have to be good when you win and when you lose".
Modric, who helped Madrid win the Champions League before leading Croatia to the World Cup final, said he wanted the duo at the event.
Thibaut Courtois added the Federation Internationale de Football Association goalkeeper award to the Golden Glove he collected in Russia for helping Belgium to third place with three clean sheets. The coach award in the women's game went to Reynald Pedros, the Frenchman who led Lyon to French league and Champions League glory.