Mohammed Salmodin has now been discharged from hospital where he was being treated for the snake bite.
Officials say he will not be charged because the reptile was not endangered.
“When I realised that a snake had bit me, I went home to get a torch and saw that it was a cobra. So I bit it to death,” he told BBC Nepali's Bikram Niraula in Biratnagar.
After he bit the snake to death, Mr Salmodin said that he went about his daily business as if nothing had happened. He says he finally agreed to go to hospital after pressure from family, neighbours and police.
The incident took place on Tuesday in a village 200km (125 miles) south-east of Nepal's capital, Kathmandu.