The call has come in an open letter to the company's board of directors on the online platform Organise, which runs workplace-specific campaigns.
The petition website purported to quote several unnamed current and former employees detailing their experiences.
The stock price spiralled down after The Sunday Times of London published a story saying female staff at the fashion brand were fed up with "forced hugging", inappropriate physical contact and sexually charged comments from Kelvin, who continues to run the company he founded in 1988.
"Plenty of people might have sat on Ted Baker's knee".
Ted Baker said it has "always placed great importance on the company's culture" and it was vital that all staff feel "valued and respected at work".
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It said Mr Kelvin greeted many people with a hug, "be it a shareholder, investor, supplier, partner, customer or colleague".
"The general feeling inside Ted Baker is that there's no official way to address the issue of harassment", the petition says. It also claims that Mr Kelvin uses sexual innuendo on a regular basis. Complaints through official channels fall on deaf ears, they say.
British clothing tycoon Ray Kelvin regularly "tries to massage people around the office, insists on long hugs with staff members, touches them inappropriately and openly asks his staff for sex", according to the petition. I went to HR with a complaint and was told "that's just what Ray's like".
The petition on Organise now has 2,459 as of Monday morning.
Shares in the fashion firm were 13.9% down at 1,573.0p in early afternoon trade. The name Ted Baker is a... "But staff won't be ignored if thousands of us stand with them".
'Accordingly, they and the board take these concerns very seriously and the board has directed a thorough and urgent independent external investigation is carried out into these matters, ' it added.