Details were later released by Pol Lt Gen Thiti Sangsawang, chief of Police Region 2, and Pol Lt Gen Itthipol Itthisaranachai, head of the Immigration Bureau.
The woman was identified only as Ms Nazu, aged 35 years, reports the Bangkok Post.
Police said she told them she was hired from Hong Kong to coordinate in the printing and posting of the giant advertisement in Thailand. All contact was via a Chinese message app and Line app, which did not show a company name.
She believed the account used to contact her belonged to the man pictured on the billboard advert.
The cost of setting up the billboard - production and space rental fees - was about B200,000. Ms Nazu said that as coordinator she earned about B17,000 per sign.
Ms Nazu was charged with being a foreigner working without a permit. She reportedly denied any wrongdoing.
The giant Chinese-language advert, offering a 30-day service for people wanting a foreign passport or citizenship, was put up over the weekend. It displayed images of passports for Indonesia, Cambodia, Turkey and Vanuatu.
It immediately drew social media attention and was taken down on Monday amid concerns of possible criminal involvement.
The billboard structure itself is reported to be owned by a Singaporean company. The local district office is investigating its legality.
The police investigation is also continuing.