The petition, which has almost 1,800 signatures, alleges that Kelvin, who launched the first Ted Baker store in 1988, regularly uses sexual innuendo, and has asked young female staff members to sit on his knee or let him massage their ears.
A petition, launched by an employee, also accuses 62-year-old Ray Kelvin of inappropriate comments and behaviour.
The allegations came to light as more than 2,500 signed an online petition calling for an end to "forced "hugging" by the CEO", calling it "part of a culture that leaves harassment unchallenged".
Atmosphere inside the Ted Baker store during the Ted Baker Wooster VIP Event on September 22, 2016 in New York City. It said that while hugs are a part of the Ted Baker culture, they are "absolutely not insisted upon".
According to the Sunday Times Rich List, Kelvin is worth £552m.
Elsewhere, the petition alleges that Mr Kelvin asked female members of staff to cuddle him, sit on his knee or let him massage their ears.
The petition notes that several staffers have left the company due to Kelvin's alleged verbal, physical, and sexual abuse, and that reporting the instances through the proper channels, like Human Resources, was "hopelessly ineffective" as reports went ignored.
Another told Organise: "The CEO always wants a hug from every member of the staff". To make things worse, when this person approached their manager about it, they said, "Don't worry if he kisses you on the neck next time, he does it with everyone".
In a statement Monday, the company announced that "an independent committee of the Non-Executive Directors has been appointed to ensure that the views and concerns are recognized and carefully considered and that appropriate responses are taken forward".
The ex-worker also describes an incident in which the CEO rubbed their shoulders in front of a group of visitors to Ted Baker's head office.
The company said the claims are being taken "very seriously" and a "thorough independent investigation" will be carried out.
Ted Baker responded by saying it has "very clear and robust HR policies".