From requiring that foreign nationals have their photos taken as part of the biometrics process to visa applicants needing to provide headshots in their applications, many Canadian immigration programs have a photo requirement.  There is no exemption from the photograph for religious reasons.  Below is a memo that was prepared for the Minister of Citizenship and Immigration Canada in 2013 confirming that there are no exemptions to the photograph requirements in response to a request for an exemption from the Amish community.

Amish and Photos