The UN says 536,000 mainly Rohingya refugees have arrived from Myanmar´s strife-torn Rakhine state since August 25, the majority of them children.
Bangladesh´s social services department said 13,751 children without a parent or parents were identified in a survey of the crowded refugee camps along its border, where charities warn that a humanitarian crisis is unfolding.
"The majority of them said they lost one or both parents in the violence in Rakhine," Pritam Kumar Chowdhury, a department deputy director, told AFP.
"Others said they didn´t know what happened to their parents, and they came to Bangladesh with relatives."
The UN has described the violence in Rakhine as a textbook case of ethnic cleansing, with displaced Rohingya Muslims in Bangladesh describing whole villages being razed, gang rapes and massacres.
Those who survived and fled to Bangladesh include an estimated 320,000 children, one-third of whom are under five years of age.
Bangladesh is building the world´s largest refugee camp — a sprawling three thousand acre (1,200 hectares) settlement — capable of housing 800,000-plus Rohingya.
Last month a junior minister asked that 200 acres be set aside in the camp for children´s facilities.
Chowdhury said an orphanage would be built for unaccompanied minors, and those without a parent would be given extra assistance and familial support.
Aid agencies have warned there is a real concern that vulnerable children could be victims of abuse or trafficking.