The three people -- whose names and ages have not been released -- died Friday as supplies were being thrown from relief trucks on the road in the Balukhali Pan Bazar near the Kutupalong refugee camp, the Inter Sector Coordination Group (ISCG) in Bangladesh said.
The deaths are a stark reminder of the desperation in the camps near the border with Myanmar, where an estimated 409,000 refugees have arrived since August 25, more than doubling the existing Rohingya refugee population.
"I could not bring anything. My clothes were given to me by someone here," said Rohingya refugee Romiza Begum. "I lost everything. There is nothing left in my home in Myanmar. Everything is destroyed."
Unofficial aid distributions are often carried out by sympathetic locals in Bangladesh, who pile bags full of donations on the back of trucks and then throw them out as they drive through the camps.
CNN witnessed several of these aid drops in and around the Kutupalong refugee camp. When the trucks are spotted on the road they spark a frenzied dash as crowds of desperate Rohingya refugees race towards them, through mud and traffic, in the hope of catching some supplies.
"We just want to help," one man throwing out aid told CNN.
Relief agencies appreciate the efforts of those trying to help, but say this is a hazardous way to do it.
Corinne Ambler, spokeswoman for the International Federation of the Red Cross (IFRC) Bangladesh, said it is better for refugees to use official aid distribution points because the truck method is too dangerous.
Refugees who manage to catch tossed supplies sometimes end up in a fight to keep them. Those who fail often climb onto the truck to try to grab anything they can, but men on the back of the truck have sticks and beat them down. Children are most in danger as the truck drivers often don't see them, Ambler said.
Many of the Rohingya refugees are sick, hungry and dehydrated by the time they arrive. Many have malnutrition or diarrhea, and some arrive with gunshot wounds, burns or land-mine injuries they sustained escaping Myanmar.
"We came to Bangladesh because life back home was very dangerous. Bullets were flying around like rain," one 60-year-old Rohingya refugee told CNN. "I fell down when I was running away and hurt my knee. I can't walk or sit properly now."
The aid agencies working in the area -- including the International Federation of the Red Cross (IFRC), the World Food Program and other UN agencies -- are forced to prioritize their limited supplies by focusing on the most vulnerable people, such as pregnant women and babies, the sick and the elderly. Ambler says the people they are serving are only "a drop in the ocean" compared to the thousands who need aid.
"I can only describe it as wall-to-wall human suffering. I've never seen anything like it," Ambler, the IFRC spokeswoman, told CNN. "We can't cope with the numbers that are here now. I don't know how we're going to cope if more come."
Three thousand families, or about 15,000 people, lined up on Friday for an official aid distribution organized by Red Crescent volunteers from Bangladesh and the UAE.
Alongside long queues of mostly women and elderly people waiting in the blazing sun, groups of men stood around looking hungry and desperate. Families headed by men and those with fewer children are a low priority, forcing many men to beg in the street.
"We have no food and no clothes. We are homeless," said refugee Mohammed Harun. "Everything, destroyed by the military. Now we are without food or blankets."
CNN cannot verify the stories of the Rohingya refugees, as access to Rakhine state is heavily restricted for journalists.
Even for the families who receive some aid, it's only just enough to keep them alive. Most aid packs include milk, juice, some semolina and some high-energy biscuits. Most of the refugees don't have any cooking equipment or electricity, so there's little point providing food that requires cooking.
Some refugees are too weak to carry food home and have to rely on volunteers to help them.
Aid agencies are ramping up their responses as fast as they can, but with thousands more refugees arriving every day, it's a race against time just to keep people in these camps alive.
"It's a challenge for everyone to scale up quickly," Ambler said. "Finally, people are starting to realize what the situation is."