The proposal to revamp the company's top leadership is one of several resolutions up for vote at the company's annual meeting, which will take place in late September in Memphis, Tennessee.
FedEx opposes the Teamsters' proposal and has urged shareholders to reject it. A similar proposal last year failed to pass after it garnered just 34 percent of the votes.
In the letter to shareholders urging them to reconsider, the Teamsters said the current structure resulted in chronic poor performance, excessive executive pay, and questionable business strategies.
Asked to comment on the letter, a FedEx spokesman referred to the company's proxy statement defending its leadership structure.
In the proxy, FedEx says its board has given careful consideration to separating the roles but feels that FedEx and its stockholders are best served by having Fred Smith, the company's founder and chief executive, serve as chairman of the board as well.
FedEx says that 11 of it 12 board members meet the independence requirements of the New York Stock Exchange and the U.S. Securities and Exchange Commission, and it disputes the union's characterization of the company's performance and Smith's pay.
This proposal, FedEx says in the proxy, is clearly an attempt by the proponent to advance its own self-interest, which is inconsistent with the best interests of FedEx and its stockholders as a whole.
FedEx's ground unit has long been criticized by critics, including the Teamsters, who dispute the company's classification of its 15,000 drivers as self-employed entrepreneurs.
Drivers at FedEx's main rival, United Parcel Service , are represented by the Teamsters.
(Reporting by James B. Kelleher; Editing by Steve Orlofsky)