Officers are treating the spraying of abusive graffiti onto the wall of the landmark late on Thursday as a "religiously aggravated attack".
Chief inspector Cherie Buttle from Greater Manchester Police said: "This is a religiously aggravated attack, which has not only caused damage to a building but has caused upset to those who attend.
"The graffiti is beneath a statue at the graffiti and, due to the size of it, someone may have noticed it happening."
The language used is too offensive to be published. A censored picture published by the Manchester Evening News appeared to show a blasphemous reference to Jesus.
Police were called to reports of criminal damage at Manchester Cathedral at around 11.45pm on Thursday - the eve of the first Emergency Services Festival of Thanksgiving at the landmark.
Speaking ahead of the event, chief inspector Buttle said: "Hopefully those attending the festival there... will be able to enjoy themselves, despite this disgusting incident."
Anyone with information should contact police on 0161 856 3221 quoting reference number 2225 of 06/09/18 or the independent charity Crimestoppers, anonymously, on 0800 555 111.
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