Messi saw off competition from Cristiano Ronaldo and Virgil van Dijk to win The Best FIFA Men's Player award, voted for by coaches, players, fans and members of the media.
But despite the 32-year-old's impressive 2018-19 campaign, boasting 51 goals, 22 assists and a La Liga title, he failed to make Arnold's shortlist.
The Socceroos coach named van Dijk his preferred player, followed by Ronaldo and Ligue 1 Player of the Year Kylian Mbappe.
Milligan meanwhile deemed new Barcelona signing Frenkie de Jong worthy of the prestigious award after a breakout, trophy-laden season with Ajax.
Messi managed second place for the veteran midfielder, who then had Tottenham Hotspur striker Harry Kane in third.
