The Edinburgh business confirmed Craig Smyth, a founding executive of Menzies Aviation, who has been with the wider company since 1993, was planning to leave his post as managing director.
Alongside that John Menzies said it is searching for a chief executive, with the board thought to favour the appointment of an external candidate.
The aviation business does ground handling at air hubs across the world, while distribution sends millions of magazines and newspapers around the UK and Ireland.
Since 2007, John Menzies has operated a three-pronged executive structure which saw each main operating division headed by separate managing directors alongside a group financial director.
Yesterday it said: "The board is conducting a detailed review of the group's senior management structure and is involved in a search process for a chief executive officer for John Menzies.
"We will make an announcement as soon as we have concluded the review process."
John Menzies has operated in the same structure since Patrick McDonald departed as chief executive in March 2007.
William Thompson, chairman at that time, suggested Mr McDonald's strong leadership and the performance of the two operating divisions meant there were fewer functions for the chief executive to look after.
Mr Smyth, finance director Paul Dollman and then distribution boss Ellis Watson were the executives placed in charge at that time.
Mr Dollman stepped down last year with Paula Bell joining as finance director in June of 2013.
From mid-2009 the distribution business was run by David McIntosh, who has been with John Menzies since 1989, but in January this year he informed the board of his intention to step down to pursue other interests.
Forsyth Black, who has been with the group for 14 years, took over that division in June this year but did not join the plc board.
Mr Smyth, 46, a chartered accountant, has been a key figure in the expansion of the fast growing aviation division.
Analysts at Liberum suggested Mr Smyth may have felt disappointed at not getting the opportunity to run the wider group.
They said: "Craig Smyth is resigning and the company has confirmed that it is looking for a [chief executive] which will return Menzies to a more conventional management structure.
"We understand the board is looking for an external candidate and we don't believe that the two events are unconnected. Whilst the loss of Craig is a negative we believe some investors will prefer the more normal structure."
Mr Smyth did not respond to phone calls. It is understood he does not have another job to step straight into.
John Menzies said: "The board of John Menzies acknowledged receipt of the resignation of one of its divisional managing directors, Craig Smyth, managing director of Menzies Aviation.
"Craig will continue in his current role and fulfil all of his contractual obligations."
According to the most recent John Menzies annual report Mr Smyth, along with other executives, has a 12- month notice period.
That same document shows Mr Smyth's basic salary for this year is more than £336,000.
For 2013, his total remuneration was £1.2 million, which included long-term incentive payments worth £646,000 and an annual bonus of £150,000.
In May, following the annual general meeting, current chairman Iain Napier suggested the business was interested in acquisitions but the focus of that activity was likely to be in the aviation arm.
John Menzies is due to report interim results next week. Liberum retained a buy rating on the stock with an 847p target price.
The shares closed up 3.5p, or 0.5 per cent at 659p.