The award is decided by a panel comprising LMA Chairman Howard Wilkinson, Sir Alex Ferguson, Paul Ince, Joe Royle, former Palace manager Dave Bassett, Barry Fry and Rachel Yankey.
Vieira and the squad were presented with a bottle of champagne and trophy today (Friday) after the 2-0 away triumph was deemed the best display of the matchweek.
Goals from Wilfried Zaha and Conor Gallagher, coupled with a resolute 90 minutes in defence, meant Palace took points from the Etihad for the third time in four meetings.
Speaking in his pre-match press conference after receiving the award, Vieira said: "It was a good day for the football club. The team performed quite well at City. It’s all about how can we maintain those performances and this is the main focus for us as a football club and me as a manager."