Morrissey says he can't perform on a show with what he called people who "amount to animal serial killers."
A&E's "Duck Dynasty" reality show follows a Louisiana family with a business selling duck calls and decoys.
A&E did not immediately respond to requests for comment from it and the Robertson family.
A person familiar with the Kimmel show's plans confirmed that Morrissey was to appear. The person lacked authority to discuss the matter publicly and spoke on condition of anonymity.
The person says Morrissey's performance will be rescheduled.
ABC says the Churchill band will perform Tuesday on Kimmel's show but declined comment on the switch.
Morrissey was treated at a suburban Detroit hospital for a bleeding ulcer last month, according to a spokesperson, forcing him to cancel a Chicago show. The diagnosis forced the former Smiths lead singer to postpone shows in Flint, Minneapolis and last Saturday at the Chicago Theatre.
His Chicago show in October was postponed because of a family medical emergency.
The Associated Press contributed to this report.