McDonald’s is not loving the idea of letting the franchisees who own and operate the majority of its restaurants pick a board member.

The fast-food chain’s board is recommending investors vote against a proposal looking to add a “franchisee director.” The proposal is considered a long shot but is garnering attention for its novelty.

“The board is against any plan to give one group or constituency the right to elect its own director to represent limited interests, which could be contrary to the long-term, best interests of shareholders,” McDonald’s said in its proxy statement issued April 13. Such a director...