The country will decide whether to accept the draft constitution in the biggest test of public opinion since the generals seized power in 2014.
A vote in favour of the charter could give the military a permanent role in overseeing economic development and politics.
It is unclear what will happen if the draft is rejected, which would raise questions about the junta's roadmap to a promised general election next year.
Polls show a large majority of Thailand's 50 million voters are undecided.
The junta, known as the National Council for Peace and Order (NCPO), has said it wants to return Thailand to democracy but to ensure politicians put the people's interests first.
Willy Fautré, director of the Brussels-based NGO, Human Rights Without Frontiers, is critical, saying, "The referendum under military control is a farce and there is no guarantee that it will be fair.
"It is just meant to boost military power as it extends too much power to the unelected NCPO, including the possibility of appointing an unelected military-backed Prime Minister."
Several MEPs, including UK Socialist member David Martin, and groups such as the Brussels based EU/Asia Centre, have also voiced concern about the constitution being voted on this weekend.
Former Thai Prime Minister Thaksin Shinawatra on Thursday also criticised the military-backed draft constitution as a "folly" that would perpetuate the power of the ruling junta and make it impossible for future elected governments to rule.
He says a vote in favour of the draft will merely subdue political parties and give the generals a permanent role in overseeing the country's economic development.
The ruling military council has said the charter will pave the way for a general election in 2017, ensure clean politics and end more than a decade of political turmoil since Thaksin, his allies and their rural supporters challenged the royalist and military establishment.
Thaksin, a former telecommunications tycoon who won the loyalty of legions of poor voters with populist policies, was toppled in a 2006 coup. He lives in self-exile to avoid a graft conviction he says was politically motivated.
Thailand's two biggest political parties, one of which is loyal to Thaksin, oppose the constitution because they say provisions are designed to ensure military supervision of politics.
The constitution would put so much power in the hands of bodies tasked with acting as counter-balances to governments that it would make Thailand ungovernable, Thaksin said.
"I predict that, even if the new government receives perfect endorsement from the present regime, it will find it impossible to manage the Thai economy or administer the country under those proposed conditions," he said.