Slym, 51, seems to have fallen from a higher floor of the hotel in Bangkok, a company spokesperson said, adding that his post-mortem will take place tomorrow. The company declined to give more details.
Bloomberg quoted a company spokeswoman to say that Slym was staying in Shangri-La hotel when the incident took place.
A British national, Slym was leading the company at a time when the auto industry was grappling with prolonged slowdown.
Expressing condolence at the sudden demise, Tata Motors Chairman Cyrus P Mistry said: "Karl (Slym) joined us in October 2012, and was a valued colleague who was providing strong leadership at a challenging time for the Indian auto industry. In this hour of grief, our thoughts are with Karl's wife and family."
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Slym was visiting Bangkok for a meeting of the Board of Directors of Tata Motors Thailand Ltd, he added.
In December, domestic car sales declined 4.52 per cent from a year earlier to 1,32,561 units. Tata Motors' sales fell about 42 per cent to 6,537 units last month.
Total sales of commercial vehicles were down 25.53 per cent to 46,757 units. The company's commercial vehicle sales dropped 45.83 per cent to 25,738 units.
Before joining Tata Motors, Slym was the executive vice president, SGMW Motors, China (a General Motors Joint Venture). Prior to that, he was president, managing director and board member of General Motors in India between 2007-11.