Stock market filings show 153,750 went for £8.12 while a further 37,500 netted £8.20.
That came just a few days after Mr Jenkinson, who has been on the board since 1986, sold around £1.63m of stock.
According to a stock market filing, both disposals this week came from Roy Nominees Limited, which is said to be a trust which Mr Jenkinson's wife, Miranda, has interests in. She is part of the Menzies family.
The stock market announcement yesterday showed Mr Jenkinson - who has founded then sold firms such as Tellydisc, Regal Hotels and contact centre operator beCogent - still has an interest in more than 4.4 million John Menzies shares, equivalent to 7.29% of the share capital.