Ronaldo's other sister Katia Aveiro posted: "Best player in the world… for those who understand football of course."
Modric won the Champions League with Real Madrid and then guided Croatia to the World Cup final in July. The midfielder was voted player of the tournament.
Ronaldo was second in the polling followed by France forward Antoine Griezmann. France's teen star, Kylian Mbappe, was fourth. Brazil star Neymar was third last year but only 12th this time. Messi was fifth in the voting, having been runner-up to Ronaldo the past two years and in the top three every year since 2007. Modric had never previously been in the top three.
Ronaldo missed out on a record sixth award, which would have moved him one ahead of Messi. The last player to win it before those two started dominating world soccer awards was Brazil midfielder Kaka with AC Milan in 2007.
"2018 is a dream year for me," the 33-year-old Modric said. "Throughout my career I realized hard work, persistence and belief in yourself in difficult moments are the foundations of success."
Modric's father was shown on the big screen wiping away tears during the ceremony at the imperious Grand Palais in Paris.
Ronaldo also won the Champions League last season with Modric, before leaving to join Juventus. He scored a hat trick against Spain at the World Cup but he failed to make an impression when Portugal lost to Uruguay in the round of 16.
- With AP