The fire broke out shortly before 19:00 CET near the area where Pep Guardiola's side had been due to enter the stadium around 30 minutes later.
Hundreds of fans had gathered outside the Etihad for a pre-match entertainment show which included on-stage interviews with City's new signings Omar Marmoush, Vitor Reis and Abdukodir Khusanov.
The show had already begun with City's female players Rebecca Knaak and Aemu Oyama on stage at the time of the fire.
The event was suspended as flames took hold of the stand and stewards moved fans away before fire services arrived on the scene.
Stewards and security staff quickly evacuated the area and a fire engine was on the scene within minutes.
The fire soon appeared to be brought under control and it was announced that the stadium was open and fans could enter.
Three entrance gates inside the cordoned-off area close to the scene of the fire were still closed.
The remainder of the pre-match show was cancelled, but the match is due to go ahead as scheduled at 21:00 CET.
Premier League champions City must beat Brugge in their last match of the opening phase to advance to the Champions League play-off round.