"The authorities have detained them to stop them from reaching their destination," said junta spokesman Colonel Winthai Suvaree.
The park "was built for Thai people to pay homage," to the monarchy, and is not designed to be used for protests or events, he added.
Rajabhakti Park in the seaside resort town of Hua Hin was built as a tribute to Thailand's monarchy by the royalist military, but it has become engulfed in a graft scandal that has undermined the junta's anti-corruption pledges.
The students said they would travel to the park and "denounce corruption," according to a Facebook post by student leader Sirawith Seritiwat, who later also announced their detention on social media.
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Thailand has had a long weekend with a bank holiday Monday to mark the King's birthday,but the park was closed at short notice.
The students were loaded onto a military bus at around midday Monday. It was not immediately known where they were taken.
Last week, two leading opposition leaders were also arrested by soldiers after trying to visit the park, which boasts seven enormous bronze statues of famous Thai kings.
Thailand's generals seized power last year partially justifying their takeover as a necessary move to curb endemic corruption among the kingdom's civilian politicians and protect the royal family.
The junta leadership, including Prime Minister General Prayut Chan-O-Cha, has insisted there was no graft involved in the park's construction, but allegations to the contrary have continued, transfixing a country where the military rarely brooks dissent.
The monarchy is shielded by one of the world's toughest lese majeste laws and prosecutions have surged since the military coup.