More than 110,000 people have become refugees in the conflict in the past 18 months, a U.N. statement said.
U.N. Special Rapporteur Tomas Ojea Quintana said the Myanmar government "must, under international law, conduct a prompt, effective and impartial investigation."
He said he received reports of Rohingya Muslims killed and injured, as well as a security guard killed, following a clash in Du Chee Yar Tan village in Maungdaw, Rakhine, and of Royingya Muslims being arrested afterward.
Violence erupted in Rakhine in June 2012, uprooting 75,000 people, with 36,000 more displaced after riots in October 2012, the statement said.
Myanmar was formerly known as Burma.