The moves against the demonstrators come after Brigadier General Thura Myint Maung, Myanmar's religious affairs minister, told Buddhist leaders that "action will be taken" to prevent further protests.
"We warn the monks and the people not to participate in protest marches. We will take action under the existing law," he was quoted as saying.
Human rights groups reported on Monday that government agents had been preparing to infiltrate the protests in order to spark trouble and justify a crackdown.
Irene Khan, the secretary-general for Amnesty International, a human rights organisation, appealed to the UN Security Council to immediately send a mission to Myanmar.
"The high risk of a crackdown against the demonstrators makes it imperative for the international community to act urgently," Khan said, adding that China, Japan and India had a role to play in ensuring stability in Myanmar.
'Pretext for crackdown'
The London-based Burma Campaign UK said it had a received reports of soldiers ordered to shave their heads, apparently to pose as monks and infiltrate the protests.
About 90 per cent of Myanmar's population is Buddhist.
At some point in their lives, every Buddhist male is expected to join the monk hood or 'Sangha'.
Every village or neighbourhood has its own pagoda and monastery, which traditionally serves as the focus for community life and the main centre for education.
In recent years rising levels of poverty have raised demand for the free education provided by the monasteries.
"They would start rioting or attacking police, providing the regime with a pretext for a brutal crackdown on protesters," the group said.
An estimated 50,000-100,000 protesters marched through the streets of Yangon on Monday in the biggest demonstration yet against the military government.
"The protest is not merely for the well-being of people but also for monks struggling for democracy and for people to have an opportunity to determine their own future," one monk told The Associated Press.
"People do not tolerate the military government any longer."
The protests were initially triggered by a massive hike in the price of fuel on August 19, but have developed into a more deeply-rooted outpouring of dissent led by groups of monks.
In the space of a month the protests have become the biggest challenge to Myanmar's military government in almost two decades.
Charles Petrie of the United Nations' Development Programme in Myanmar told Al Jazeera the demonstrations were an expression of the frustrations felt by many in the country after years of poverty and hardship.
"The monks have brought out into the open the issues that are of real concern to a significant portion of the population," he said.
"There is an underlying suffering that is now being expressed."