Things then took a turn for the worse for Arsenal when Danny Welbeck limped off after picking up a knee injury, possibly ruling him out of Euro 2016.
Kevin De Bruyne then gave City the lead just after half time before Alexis Sanchez fired home the equaliser after a sublime lay-off from Giroud.
Both sides pressed towards the end of the clash but failed to find the winner.
The draw leaves Arsenal in third place, three points ahead of City in fourth.
City’s Champions League hopes are out of their hands now with just a week left in the season.
Manchester United have a game in hand on both sides, against West Ham and Bournemouth within the next week.