The pro-democracy leader's party says the constitution will enshrine military rule, and condemned the government for focusing on its referendum rather than on delivering aid to cyclone victims.
The cyclone left at least 133,000 people dead or missing and about 2.4 million people remain in desperate need of food, shelter and medicine.
Al Jazeera's correspondent in Myanmar, who is not being named for security reasons, reports from the Irrawaddy Delta region that many people have still received no assistance.
"It is not difficult to find people who really need help - they haven't had doctors or any aid, surviving off coconut for the past three weeks," she said.
The villagers have also complained of intimidation in Saturday's poll, saying military officers came to their homes and ordered them to vote.
"Villagers can't tell you what the vote is about. People are angry but really cautious, very careful not to speak out and get themselves in trouble," she reported.
"A month ago the government man came to my house and took a photo of everybody in my family," one government worker told Al Jazeera.
"Those who vote yes get opportunities, licenses for bikes cars and businesses. I've heard of people being taken to prison for voting no. It's intimidation."
Another woman said: "It's bad. people in the [Irrawady] Delta are being made to vote when they are suffering."
Relief could finally be on the way after Ban Ki-moon, the UN secretary-general, met Than Shwe, Myanmar's senior general.
The military leader on Friday agreed to allow access to all foreign aid workers to help with the relief operation after earlier refusals.