The company said Mr McIntosh, 51, wanted to pursue other interests but was happy to remain in post until a successor had been recruited.
The departure follows that of finance director Paul Dollman last May after 11 years, leaving only aviation managing director Craig Smyth of the triumvirate that has run Menzies since June 2009, when its shares were at 131p. The shares were up 3.5p yesterday at 715.5p.
Mr McIntosh joined the main board at Menzies when he succeeded Ellis Watson as managing director of distribution in June 2009. He had already handled the long-running inquiry by the office of Fair Trading into the industry and piloted the acquisition of ancillary business Orbital Marketing, and he quickly took the business into unexpected growth mode on the demise of competitor Dawson in August 2009, which helped turbo-charge Menzies' recovery. In the past year the division has delivered contract renewals to 2017 with all the major publishers and despite structural decline it has rarely disappointed the market with its performance, largely due to an ongoing efficiency programme.
The group dispensed with a chief executive to move to its unusual structure in May 2007. Mr Dollman became chairman of Smart Metering Systems last November, while Mr Watson moved in quick succession to FirstGroup, SyCo, and DC Thomson where he became managing director in 2011.
Mr McIntosh's first role was in Menzies' finance department, he joined the business in 1998 as finance director and then commercial director. An observer said: "He has completed 25 years and has had five tough full-on years in the role, he probably feels he has another big role in him."
Ian Napier, chairman of John Menzies, praised Mr McIntosh's "outstanding contribution" during a long career, and said a search for a successor would begin shortly.