Thailand's monarchy is protected from any criticism inside the kingdom by a harsh lese majeste law, use of which has skyrocketed since the military seized power in 2014.
Vajiralongkorn, 64, ascended the throne on Thursday, seven weeks after his widely revered father King Bhumibol Adulyadej died after 70 years on the throne.
The military authorities have vowed to pursue critics of the royal family at what is a delicate transition for the monarchy given Vajiralongkorn does not yet boast the widespread popularity of his father.
"Pai was arrested this morning and is in police custody now," Sunai Phasuk, a researcher with Amnesty International's Thailand office told AFP.
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Police did not respond to requests for comment.
But a copy of the arrest warrant seen by AFP showed the filing was made by a court in the northeastern city of Khon Kaen.
In a statement published on Facebook, the anti-junta New Democracy Movement confirmed Jatupat's detention, adding the arrest was over a profile of Vajiralongkorn he had shared on Facebook.
"This is a severe violation of the principle of human rights and contradicts the principle of freedom of expression under a democracy," the statement added.
Media inside Thailand must heavily self-censor when covering the monarchy.
Vajiralongkorn's ascension has been met with hagiographies in the Thai press and quotes from locals who are reported to be overjoyed.
However the arch-royalist junta has struggled to tamp down dissent online.
While critical reporting on Vajiralongkorn is curbed inside the kingdom, most Thais are aware of his colourful lifestyle, his three marriages and some of the uncensored overseas articles that have been published about him, largely thanks to social media.
But posting such articles can be perilous.
Last year a woman was sentenced to a record 30 years in jail for six comments she made on her Facebook account that were deemed critical of the monarchy.
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