The newspaper cites witnesses who said that an argument broke out between two groups of Thai youths at Zoom Bar on Haad Rin Beach.
A member of one of the groups reportedly fired a shot into the crowd as he ran out of the bar, hitting Mr Ashton in his torso.
Police have reportedly arrested a 26-year-old suspect and plan to question him at Noon on Wednesday.
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Addressing an audience in America, the former PM said of Europe's single currency that it was not working "as intended".
The countries lawmakers voted to impeach President Park Geun-hye in the wake of mass protests against her.
The former presidential candidate, who has herself been the target of false news reports, said such stories had 'real-world consequences'.