The Gunners were looking to keep their faint titles hopes alive at the City Ground but Taiwo Awoniyi's first half strike ensured safety for Steve Cooper's men and kill off Arsenal's title aspirations.
City still have three games to play, starting against Chelsea on Sunday, but are four points clear of Arsenal, who have one game left.
Pep Guardiola's side have now emerged champions in five of the last six Premier League seasons.
They are in contention to claim a remarkable treble, with FA Cup and Champions League finals still to come against Manchester United and Inter Milan respectively.
Arsenal can comfort themselves with a second place finish, which means a return to Champions League football for the first time since the 2016/2017 season.
Mikel Arteta's side led the table for much of the campaign but a run of just two wins in their last eight matches have culminated in missing out on a first Premier League title since 2004.
