The Egyptian striker picked the ball up on the edge of the Everton box, breaking free of his marker before curling a left-footed strike into the top corner.
It's the first time since 2006 that Barcelona icon Lionel Messi has not been among the candidates for FIFA's top award, and also the first time someone else won the award outside Messi or Ronaldo. Thanks to those who voted for me.
I would like to give congratulations to Mohamed [Salah] and Cristiano [Ronaldo] for the great season that they had.
Brazil's Marta collected her sixth women's player of the year award, but her first since 2010 after finishing as runner-up on three occasions during the intervening years, while former Chelsea keeper Thibaut Courtois was named goalkeeper of the year.
The impending absence of Ronaldo from Monday's gala has further fueled speculation that the 2018 ward is for Modric. Ronaldo also scored a memorable hat-trick in the FIFA World Cup but did not progress beyond the round of 16.
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We are going to play better than we did but I think it's going to be a very hard season. All of them, they can say the same thing.
"This trophy is not just mine, it's for all my Real Madrid teammates, for all my teammates from the Croatia national team".
Salah has got ahead of himself, however, while making his acceptance speech for the Puskas Awakard, which is awarded to the best goal of the year.
In other categories, the Best Coach award looks destined for Didier Deschamp after his World Cup victory with France, though there is also competition from Zinedine Zidane to retain his crown.
Best Goalkeeper award: The best goalkeeper was by Belgian worldwide and Chelsea goalkeeper, Thibaut Courtois.
Best Women's coach: Reynald Pedros, coach of Lyonnais Féminin - who won the French league and the Women's Champions League last season - picks up the award.
A list of 15 nominees will be selected by France Football and a panel of global journalists will vote on a victor.