The incident happened near the Irrawaddy delta town of Bogalay, one of the regions worst hit by Nargis.
"The crew steered to an island but the boat sank rapidly. All crew members, including four Myanmar Red Cross relief workers on board ... managed to get to safety," the Red Cross statement said.
"Apart from the delay in getting aid to people, we may now have to re-evaluate how we transport that aid," Michael Annear, Red Cross's disaster manager in Yangon, said.
The news of the boat's loss came as Oxfam, another international aid organisation, said up to 1.5 million cyclone survivors could die if clean water and sanitation are not provided to them.
Sarah Ireland, Oxfam's regional chief, said the toll from Nargis could eventually be 15 times higher than their latest estimate of 100,000.
"In the Boxing Day tsunami [of 2005] 250,000 people lost their lives in the first few hours, but we did not see an outbreak of disease because the host governments and the world mobilised a massive aid effort to prevent it from happening," she said.
Diplomats in Yangon, Myanmar's former capital, say up to 100,000 people may have been killed by Nargis, while more than one million have been left without shelter.
Search for food
Survivors have begun to pour out of the Irrawaddy delta in search of food, water and medicine.
Aid workers cautioned that thousands of them will die if emergency supplies do not get through soon.
Buddhist temples and schools in towns on the outskirts of the affected areas have become makeshift refugee centres for women, children and the elderly.
The Myanmar government is accepting aid from the outside world, including the UN, but officials have made it clear that they will not let in foreign logistics teams who are needed to transport the aid into the delta.
"Unless there is a massive and fast infusion of aid, experts and supplies into the hardest-hit areas, there's going to be a tragedy on an unimaginable scale," Greg Beck from the International Rescue Committee said.
The warnings came as the ICRC said a cargo aircraft carrying emergency aid had landed in Myanmar on Sunday.
The cargo includes medical supplies to treat 250 trauma patients and basic health care for 10,000 people over three months.
The cargo also contains a mobile water-treatment plant and sanitation items to provide drinking water for 10,000 people, as well as body bags.
The supplies are for several detention facilities hit by the cyclone.
The ICRC, which has been facilitating family visits to prisoners in the country over the past few years, says Myanmar's government asked the organisation to help.
Myanmar's government has refused to allow foreign relief workers into the country to direct relief efforts.
Humanitarian officials are still waiting for visas a week after the cyclone struck.
The UN, which has appealed for $187 million in aid, is not confident that the food, water, medicines, bedding and utensils already flown in to Myanmar will make it to those in need.
Australia dramatically increased its aid contribution to the cyclone victims, pledging an extra A$22 million to take its total offer to A$25 million ($23.4 million).
WFP shifts office
On Sunday, the World Food Programme said it was moving aid down to its field headquarters in Labutta, a Delta town, using trucks provided by aid partners.
Marcus Prior, a WFP spokesman in Bangkok, said the agency has flown in seven shipments of aid, and an eighth is due to land on Sunday.
|State media said election officials are counting|
the results from Saturdays vote [AFP]
The WFP said that its food shipments had been briefly impounded on Friday at Yangon airport.
On Saturday, Myanmar's government pushed ahead with a controversial referendum despite international appeals for the ruling military to focus on relief efforts.
The referendum got under way in much of the north and far south of the country, although in the areas hardest hit by Cyclone Nargis the vote has been postponed for two weeks.
Some 27 million of Myanmar's 57 million people were eligible to vote, although it was unclear how many voted and how many will vote on May 24 instead.
State media said election officials are "systematically and accurately" counting the ballots, but did not indicate when the results will be released.