Some 3m people died during the five-year conflict which pitted government forces supported by Angola, Namibia and Zimbabwe against rebels backed by Uganda and Rwanda.
Slogans
The BBC's Arnaud Zajtman in the capital, Kinshasa, says the unrest in Moba began in the early hours of the morning with people shouting anti-Tutsi slogans.
The UN's offices were then targeted and some vehicles destroyed.
Some 16,000 UN troops are in DR Congo - the world's largest peacekeeping force.
The Tutsis, known in DR Congo as the Banyamulenge, fled Moba to neighbouring countries during the war.
There have been recent rumours in the area that the UN refugee agency is assessing whether the Banyamulenge should return home.
Our correspondent says the Banyamulenge feel there is growing anti-Tutsi feeling the country.
In nearby North Kivu province, Banyamulenge leaders recently issued a communique saying they feel insecure after eight members of their community were killed, he says.
Tensions have been growing in the east where renegade Tutsi army officer Gen Laurent Nkunda is leading a rebellion.
He has refused to fully integrate his forces into the national army, citing a need to protect the Tutsi population.