A petition, launched by an employee, also accuses 62-year-old Ray Kelvin of inappropriate comments and behaviour.
The company said: 'Ray greets many people he meets with a hug, be it a shareholder, investor, supplier, partner customer or colleague'.
Ted Baker said yesterday that an independent committee of non-executive directors had been appointed to ensure that the views and concerns mentioned in the petition are considered and appropriate responses are taken.
Hitting back at the allegations, the company said that the issues raised via the petition were at odds with the core values of the business and its CEO.
Another complaint made in the petition is that previous complaints have been ignored.
Shares of Ted Baker, which operates almost 500 stores worldwide, plunged 15 percent on the London Stock Exchange to a five-year low on the news. It said that while hugs are a part of the Ted Baker culture, they are "absolutely not insisted upon". It says the company's human resources department (HR) has not acted on claims, saying: "Many of the staff have reported [Kelvin] to HR, but HR keep saying "that's just what he's like". "He would hug several people a day and it would be very uncomfortable".
It says Kelvin "tries to massage people around the office, insists on long hugs with staff members, touches them inappropriately and openly asks his staff for sex".
The company said that it was now "in dialogue" with Organise in order to "understand the details and nature of the claims".
It promised that a "thorough independent investigation" into the claims would be carried out.
Kelvin, who keeps a low profile and refuses to have his face photographed, is ranked at number 244 on the 2018 Sunday Times Rich List. Pursuing the issue through HR had been "hopelessly".
It has 544 stores, concessions and outlets worldwide and offers merchandise ranging from men's and women's wear to accessories, children's wear and items for the home.