Ban Ki-moon said on Thursday he is "deeply concerned about the welfare of the people of Myanmar" at what he said was a "time of national tragedy".
Myanmar's government has said it will postpone the referendum for two weeks in 47 towns and cities, including the city of Yangon and parts of the hard-hit Irrawaddy delta area.
But it is calling is calling on citizens in other parts of the impoverished nation to turn out and support the referendum,
The referendum is designed to win support for a constitution drafted by the military and reports in state-run media have made it clear that it is a national duty to vote "yes".
Myanmar's ruling generals say the constitution, which has taken them 14 years to draw up, is a key step in what it calls a "roadmap to democracy", paving the way to elections in 2010.
But critics say the document is a sham intended to legitimise the generals' hold on power.
Myanmar's opposition National League for Democracy (NLD) party, led by detained Nobel peace laureate Aung San Suu Kyi, has called for the government to postpone the referendum.
"With this situation, it is not the appropriate time to hold the referendum," Nyan Win, NLD spokesman, told the AFP news agency.
The NLD and other pro-democracy groups in the country have had little ability to campaign for a "no" vote as the government has outlawed speeches and leaflets about the referendum.
The referendum will be the country's first ballot since the May 27, 1990 election which the NLD won by a landslide.
The government refused to recognise the results and launched a bloody crackdown on student-led street protests.
The ruling military has been impervious to appeals to allow international monitoring of the referendum.
Earlier this year it told Ibrahim Gambari, the UN's envoy for Myanmar, that the country would not allow outsiders to interfere with its sovereignty.
Gambari made a number of visits to Myanmar in the aftermath of protests in September last year that killed at least 31 people and left large numbers missing.
In 2005 Myanmar's ruling generals increased their isolation from the rest of the world and their country's own population by moving the capital from Yangon, Myanmar's biggest city, to the new, purpose-built city of Naypyidaw in the north of the counrty.
Local rumour ascribed the move to the advice of fortune-tellers, who foretold revolt and disaster in Yangon.