Stephane Jaquemet, the Nepal representative for the U.N.'s High Commissioner for Refugees, said the two camps housed refugees from Bhutan.
"Fire in two camps on the same day is a disaster," she said.
An estimated 3,790 in the Goldhap camp lost their homes while 1,200 homes burned in the Sanischare camp, the UNCHR reported Wednesday.
Jaquemet said the fire at the Goldhap camp engulfed the health center, school and most other sections,
The cause of the two fires was being investigated.
Officials said fire spreads rapidly in the camps where huts made of wood, bamboo and thatch are packed close together.
The threat of fire is particularly acute during Nepal's dry season.