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The Portugal international won the award following a vote comprised of the public, the 20 Premier League club captains, and a panel of football experts.
Dias played a part in 15 clean sheets for City, and was on the winning side in 23 of his 32 League appearances, also earning himself a spot in the PFA Team of the Year.
The centre-back won two trophies during his first campaign in England - the League title and Carabao Cup - but ended up on the losing side in the Champions League Final as Chelsea beat City 1-0 in Porto.
Dias follows in the footsteps of team-mate Kevin De Bruyne, who won the award last year.
Dias is also only the fourth defender in Premier League history to win the award, and the second Portuguese after Cristiano Ronaldo in 2007 and 2008.