Slym, 51, died after the fall from the hotel in Yannawa district, police were quoted as saying on the website of The Nation newspaper.
Police said they were alerted at 7.45 am that a "foreigner fell from the 22nd to the fourth floor" of the hotel, the report said. It was reported that "police found a suicide note" in his room and his wife was still in shock.
Bloomberg quoted a company spokeswoman to say that Slym was staying in Shangri-La hotel when the incident took place. His post-mortem will take place tomorrow, the company said without giving more details.
A British national, Slym was leading the company at a time when the auto industry was grappling with prolonged slowdown.
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He joined the auto major in 2012 as part of a major management overhaul and was responsible for charting the company's strategy to regain momentum in the Indian market.
Slym was visiting Bangkok for a meeting of the Board of Directors of Tata Motors Thailand Ltd, he added.
As part of a restructuring exercise, Slym last week had announced a voluntary retirement scheme for a section of employees to rationalise costs.
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.
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 during 2007-11.
For over two decades, Slym was with Toyota and General Motors in various positions across geographies.