The council was given the Special Award at the annual event at the Hilton Leeds City Hotel, which recognises outstanding achievement in and around the region in the previous 12 months.
Six people from Yorkshire lost their lives in the attack on an Ariana Grande concert at the Manchester Arena in May.
The award was accepted by Sir Richard Leese, the leader of Manchester City Council, who said: “The Manchester Arena attack on May 22 was a terrible event which we will never forget.
“We were overwhelmed by the messages of solidarity from around the world and this award is a touching reflection of the spirit in which our friends from across the Pennines stood together with us.
“As a city we were determined not to allow those who want to make us frightened and divided to succeed. We were equally determined to ensure that all those affected by the attacks - whether through bereavement, injury or trauma - know that they remain in our hearts.
“I’m proud of the way the city as a whole responded and how the council and its public sector partners helped to set the tone, demonstrate resilience and compassion and provide support for those affected.”
Elsewhere, Huddersfield picked up three of the nine awards on offer, with Huddersfield Town Operations Director Ann Hough named Yorkshire Woman of the Year in the year the club reached the Premier League.
Cricketer Ryan Sidebottom received the Sporting Achievement award and Huddersfield Choral Society won the Arts and Entertainment award.
Leeds City Council’s chief executive Tom Riordan was named Yorkshire Man of the Year and there was a Lifetime Achievement award for former cricket umpire Harold ‘Dickie’ Bird, from Barnsley.
Ryan Sidebottom’s award coincided with him retiring as a professional cricketer after a two-decade career which brought him five county championship titles with Yorkshire and Nottinghamshire, 22 Test caps for England and well over 1,000 wickets in all forms of the game.
He said: “It’s a great honour and I’m humbled and delighted to win this award. It’s a reflection on my career, I guess, but you don’t think about this kind of thing during your career. Instead you just try to contribute to the team, try to be a good guy and pass on your knowledge when you can.”