Police found roughly three grams (0.1 ounces) of marijuana.
"We didn't know who he was when he was first arrested because he had a normal passport, nothing identifying him as a VIP," Police Colonel Jirasak Siemsak told AFP from Phuket.
Shah, who is free on bail, denies the charge. If convicted he faces a light sentence because marijuana possession for personal use is not considered a serious offence in Thailand.
"If he confesses he may get a suspended sentence," Jirasak said, adding that police were awaiting the results of a drug test but expected to pass the case on to prosecutors soon.
Shah became heir to the throne in 2001 after his cousin, former crown prince Dipendra, killed nine members of his family including the king and queen in a drink-and-drugs-fuelled rampage before apparently turning his gun on himself.
Nepal abolished its monarchy in 2008.