"One soldier and 10 police sacrificed their lives for the country," Commander in Chief Min Aung Hlaing said.
"21 militants have been killed in the fongoing battl," Hlaing added.
Authorities alleged that an estimated 150 Rohingya insurgents attacked at least 20 police outposts and an Army base, but "soldiers fought back."
"Fighting remains in some locations and combined forces of the Tatmadaw (Myanmar armed forces) and police forces are still waging an attack against the extremist terrorists," the State Counselor Office's Information Committee said on Facebook.
An insurgent group known as the Arakan Rohingya Salvation Army, formerly known as Harakat al-Yaqeen or "Faith Movement" has claimed responsibility for the attack on Twitter.
"This is a legitimate step for us to defend the world's persecuted people and liberate the oppressed people from the hands of the oppressors!" the group said.
Rakhine State is home to the Rohingya community of Myanmar, ethnic Muslims, who have long faced persecution in the Buddhist-majority country, especially from the country's Buddhist extremists.
The Rohingya are denied citizenship and are seen by many in Myanmar as illegal immigrants from Bangladesh, despite claiming roots in the region that go back centuries, with communities marginalised and occasionally subjected to communal violence.