He said his security detail was removed, and his phone and Internet service had been cut.
The head of the armed forces visited the prince yesterday and warned him over actions that people familiar with the matter said could be related to a plot to destabilise Jordan, and several high-profile figures were detained.
The alleged plot "included at least one other Jordanian royal as well as tribal leaders and members of the country's security establishment", the United States daily added.
Labib Kamhawi, a Jordanian analyst, told the Associated Press that Hamzah likely crossed a line for the royal family by indicating he might be an alternative to the long-ruling king.
Prince Hamzah is not seen as a major threat to Jordan's monarchy and has been marginalised for years, but the move against him represents the first such incident involving a close member of the royal family since King Abdullah came to the throne.
Hamzah, 41, is the son of Hussein and Queen Noor, his American-born fourth wife.
Mr Safadi said that a "foreign intelligence agency" had been in contact with Prince Hamza's wife to supply them with a plane out of the country.
Jordan arrests ex-palace aide, others for ‘security’ reasons
While Hamzah denies any wrongdoing, he denounced the ruling government in the video, saying, "I am not the person responsible for the breakdown in governance, for the corruption, and for the incompetence that has been prevalent in our governing structure for the last 15 to 20 years, and has been getting worse by the year".
He denied being part of "any conspiracy or nefarious organisation", but said the country of 10 million people had "become stymied in corruption, in nepotism and in misrule" and that no one was allowed to criticise the authorities. He did not identify the "foreign parties" allegedly involved in the plot.
Jordan's army chief said on Saturday that Hamzah was not under arrest, but had been asked to stop "some activities that could be used to shake the stability and security of Jordan".
Jordan has few natural resources and its economy has been hit hard by the Covid-19 pandemic. Jordan made peace with Israel in 1994.
Kuwait's foreign ministry expressed its support to all measures taken by King Abdullah and his crown prince to maintain the security and stability of Jordan, adding "the security and stability of the kingdom are that of Kuwait".
"Jordan's security and safety is a fundamental basis for the security and safety of the Arab world", Lebanese Prime Minister designate Saad al Hariri said on Twitter.
In early 2018, as then-President Donald Trump was threatening to cut aid to countries that did not support US policies, the administration boosted assistance to Jordan by more than $1 billion over five years.
Abdullah stripped his half-brother Hamzah of his title as crown prince in 2004, saying he had chose to "free" him from the "constraints of the position" in order to allow him to take on other responsibilities.