The dangers posed would be exacerbated by wet and muddy conditions brought on by the upcoming rainy season, said Rownak Khan, UNICEF's deputy representative in the country. Nepal's monsoon season normally runs from June to September.
The confirmed death toll from the 7.8 magnitude quake which devastated the densely-populated Kathmandu Valley on April 25 has risen above 6,200, with more than 14,000 injured, according to the Nepali government.
There was no number for the missing, but bodies were still being pulled from the debris of ruined buildings, and rescue workers have not been able to reach some remote areas.
"Hospitals are overflowing, water is scarce, bodies are still buried under the rubble and people are still sleeping in the open," UNICEF's Khan said in a statement. "This is a perfect breeding ground for diseases."