The clashes late on Wednesday lasted for five-hours and were among the most serious involving UN troops deployed in the volatile region to quell ethnic fighting and protect civilians.
"The attacks came from two separate spots in the south and one from the east. One Bangladeshi soldier was shot in the leg but survived," UN spokesman Leocadio Salmeron said.
Despite an April peace deal to end the country's five-year civil war, fighting has continued to spread terror and claim lives in Congo's lawless east.
UN troops deployed in Bunia in September with a mandate to patrol the surrounding mineral-rich district of Ituri and prevent clashes between rival Hema and Lendu militias.
More than 50,000 people have been killed in Ituri since 1999.