The boss of the pizza delivery business has been struggling in recent years to win over franchisees, who have been demanding a bigger slice of profits.
Chairman Stephen Hemsley also announced that he will step down once a replacement is found for the role, which the 62-year-old has held for 11 years. Hemsley has been on the board of Domino’s in different jobs for 21 years, but new guidelines say executives should spend no longer than nine years on a company’s board.
The announcements come as Domino's revealed that sales in the six months to 30 June rose 4.7 per cent to £645.8 million, with pre-tax profits sliding 27 per cent to £30.5m. On the company's preferred measure, adjusted pre-tax profits were down 7.4 per cent to £42.3m.
UK like-for-like sales were up 3.9 per cent in the period, although this was a slowdown on the 5.9 per cent rise during the same period a year ago.
And international performance - in Sweden, Norway, Switzerland and Iceland - "remains challenging", bosses said, with operating losses stretching to £6.4m - compared with a £1.8m loss a year ago.
But the ongoing issue with franchisees is expected to concern investors, even with the departure of Wild.
The company said: "Against the backdrop of ongoing discussions with our franchisees, we are seeing franchisees delay opening new stores. This means that we are unable to give guidance on the number of new stores this year, although we continue to expect a materially lower number compared to 2018."
Just seven new stores were opened in the UK during the period. By comparison, 40 new stores opened in the first half of 2017 before the franchise problems arose.
Wild said: "The relationship with our UK and Ireland franchisees is very important to the long-term sustainable growth of the system.
"We are actively involved in detailed discussions and are giving these considerable focus and attention.
"Whilst dialogue is continuing, new store openings are being delayed and some of our working practices are being impacted.
"The situation is complex, and we expect resolution will take some time, likely into 2020. We are committed to working with our franchisees to agree sustainable win-win solutions."
Some franchisees have privately blamed Wild's brash management style for a breakdown in relations, although the company insists co-operation is improving.
Despite the problems, customers were still keen to eat pizzas, with online orders growing to 82 per cent of sales. In the UK, online orders were even higher at 90.7 per cent.
However, bosses revealed that the number of customers using a discount code for their order rose from 88.1 per cent to 89.6 per cent.