"It's a brilliant feeling and a great honour for me," Dunnie told the City website. "I'm really proud that the fans have voted for me, and I want to say a big 'thank you' to them.
Goalkeeper Joe Hart scooped the Young Player award, while youngster Ben Mee, who captained the Under 18s to the Blues' first FA Youth Cup win since 1986, was named Most Promising Player.
"The team's improved an awful lot this season," added Dunne. "Joe Hart has won the Young Player award and has had a superb year.
"Martin and Vedran came in at the start of the season and did very well, and Elano was the one who really stood out at the start of the season.
"I think everyone's done well at different times throughout the season and could have had a shout at some time.
"The fans have enjoyed the type of football we have played in most of the games here this season, and there's been a big improvement on last season."