Shares in FastJet were down 7.8 per cent in mid-afternoon trading.
Haji-Ioannou owns around 12 per cent of FastJet's stock through his company EasyGroup, which is the licensor and brand owner of FastJet. He has been embroiled in a war of words with the airline over the past few months, and in March threatened the company with legal action over a series of alleged licence breaches.
Among the charges Haji-Ioannou lays out in his letter to shareholders is the allegation that Child had "burnt through" $25m (£18m) of the compny's money. Haji-Ioannou also said that EasyGroup had requested that FastJet move its headquarters from Gatwick to Tanzania but "nothing has happened on that front yet".
"We have had numerous discussions with Colin Child since his appointment and, quite simply, do not believe he is the right man for the job," said Haji-Ioannou.
"Chairing an airline (even a tiny one like FastJet) is a serious and complicated business and doing it from almost 5,000 miles from its centre of operations and customers is ridiculous."
The entrepreneur went on to state that EasyGroup believes its disputes under the brand licence have been "fabricated" by Child "in order to divert attention away from his own failures".
"He is trying to say that somehow I do not want the shareholders of this company to do well... Remember I have put more money into this business than any other person ( excluding the fund managers who are using other people’s money)," Haji-Ioannou said.
"Colin Child has also started rumours that I am trying to lower the share price to buy the company on the cheap. Nothing is further away from truth."
He added that in order to confirm that EasyGroup was not interested in purchasing the African firm, he was using his letter to investors to declare here and now that "we have no intention to bid for FastJet and will not bid for this company for a period of one year from today per the rules in the Takeover Code about put up or shut up, subject to any material change in circumstances".
"I am a great believer in shareholder activism. I have created shareholder value before by targeting companies under weak management and where that management, to add insult to injury, has continued to be handsomely paid. There is nothing better to focus the mind of a director than a general meeting to remove him/her from the board," Haji-Ioannou said.
FastJet has been contacted for comment.