Flooding in neighbouring India, as well as in downstream Bangladesh, has also caused widespread damage and impacted millions.
"Police are working with other agencies and locals to find the missing people," Nepalese police spokesman Dan Bahadur Karki told AFP.
Those killed and missing are in multiple locations.
Monsoon rains from June to September bring widespread death and destruction every year across South Asia, but the numbers of fatal floods and landslides have increased in recent years.
Experts say climate change and increased road construction are exacerbating the problem.
Parts of Nepal have been receiving heavy rainfall since Thursday, prompting disaster authorities in the Himalayan nation to warn of flash floods in multiple rivers.
There have been reports of inundation in several districts of lowland areas bordering India.
Last month 14 people were killed in Nepal in ferocious storms that brought landslides, lightning and flooding.
In India, floods have swamped the northeastern state of Assam, with six people killed in the last 24 hours, Assam's Disaster Management Authority said Sunday.
That takes the death toll from the downpours since mid-May to 58.
In low-lying Bangladesh, downstream from India, the disaster management agency said floods had impacted more than two million people.
Much of the country is made up of deltas where the Himalayan rivers the Ganges and the Brahmaputra wind towards the sea after coursing through India.
The summer monsoon brings South Asia 70-80 percent of its annual rainfall.
burs-pjm/smw
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