Two police officers led 43-year-old Umaporn Sarasat to a picture of King Bhumibol Adulyadej and told her to get down on her knees and bow towards the picture.
A 500-strong crowd, some holding images of the revered monarch, jeered when she left the police station, and had to be held back by police officers linking arms.
The public humiliation happened on Sunday in Koh Samui, a palm-fringed island resort popular with British tourists.
It was the latest of several such incidents since King Bhumibol died last week after a reign of 70 years, plunging Thailand into intense mourning.
Small business owner Ms Sarasat was said to have posted disrespectful comments on Facebook.
Some reports said she criticised King Bhumibol, while others said the comments were directed at his son, Crown Prince Vajiralongkorn.
It is likely she will face charges of insulting the monarchy.