Modric, who played alongside Kane a brief number of times in his last season at White Hart Lane, picked up the prize to become the first player other than Cristiano Ronaldo or Lionel Messi in 11 years to be honoured.
The Croatian, who enjoyed a fine season with Real Madrid before helping to guide his country to the World Cup final, was joined by Ronaldo and Liverpool's Salah.
Kane plumped for Ronaldo and Messi and completed his three-man shortlist with Manchester City's Kevin De Bruyne, largely regarded as the reigning Premier League champions' best player throughout last season.
Salah scored 44 goals in his return to the Premier League with Liverpool as the Reds finished fourth in the division, behind Kane's Tottenham, and reached the Champions League final.
The Egyptian, who failed to best the FIFPro XI, was rewarded with the Puskas award for best goal for his strike against Everton last December.