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.
More top news
US President talks about meeting Royal toddler in his last address at the annual White House correspondents' dinner.
Clocks will go forward 30 minutes so there is half an hour more daylight in the evening when energy consumption peaks.
Tina Green is to be called before the Work and Pensions Committee as it looks into how the high street chain went into administration.