The junta postponed the referendum in Yangon, the country's largest city, and the rest of cyclone-hit southern Myanmar. It plans to call people in those areas to vote May 24.
The people of Myanmar, also known as Burma, have not voted in nearly two decades. The last elections were in 1990, when Suu Kyi stunned the regime by winning in a landslide; the generals annulled the results and jailed many of the victors.
Government workers say they were told that voting "no" in the referendum would cost them their jobs.
But the digital revolution has given opponents a relatively safe way of urging a "no" vote. Cell phones were beeping a barrage of instant messages as people in Yangon asked family and friends in other parts of the country to reject the draft constitution.
In addition to the ban on Suu Kyi, the constitution would bar thousands of her supporters from public office because they have been charged with crimes under the regime's draconian security laws, which include a ban on gatherings of more than five people.
The constitution explicitly says that the military must "be able to participate in the national leadership role of the state" and would give the commander in chief the power to appoint one-quarter of the members of both houses of Parliament, which would give the military veto power over any legislation.
The Associated Press contributed to this article.
