Held to celebrate His Majesty’s 88th birthday, the event is scheduled to take place on December 11.
HRH Crown Prince Maha Vajiralongkorn will lead the bicycle parade in Bangkok.
Prawit said evidence of the plot had come to light in the form of phone texts and also LINE chat app messages.
As the deputy prime minister overseeing security affairs, Prawit said the public could have faith in the safety measures implemented by authorities during the event.
Meanwhile, Prime Minister General Prayut Chan-o-cha warned that posting social media messages of incitement was a legal offence under the computer-crime law.
He added that, by taking legal action against such offenders, his administration is simply enforcing the law, not violating human rights.