Archbishop Bernard Hebda addressed the controversy in a letter.
He said he'll refuse to receive a vaccine if one is developed.
Michel Mulloy was due to take up his new role on Oct. 1.
The diocese will allow churches to resume in-person mass next week.
The priest who made the comments has said he's sorry his words were hurtful to Muslims.
It follows an in-depth investigation and research effort by ProPublica.
John Nienstedt resigned in disgrace from the archdiocese in 2015