The junta, which ousted Thaksin Shinawatra, the twice-elected prime minister, in September last year, says the charter will pave the way for new elections later this year.
Democracy advocates argue that it rolls back reforms and could allow the military to hold sway over future governments instead.
Campaigning is tilted heavily in the government's favour, with half the country under martial law and a new law threatening prison for anyone convicted of obstructing the referendum.
If the charter fails, the generals can impose one of Thailand's 17 previous constitutions and amend it as they please.
But a rejection of the charter could reignite political tensions, delaying elections and injecting fresh uncertainty into Thailand's wobbly economy, analysts say.