Rakhine state has been in a turmoil since August 25 after Rohingya militants launched deadly attacks on police posts.
Border Guard Police Maj. Zayar Nyein told Associated Press that two of the graves, that were found on Monday, contained bodies of 20 females and eight males.
The government's Information Committee said on its Facebook page that all eight males were boys, including six who were under 10 years old. It said another mass grave was discovered 200 meters away on Monday that contained the bodies of 17 more Hindu villagers.
Police have blamed the Arakan Rohingya Salvation Army insurgent group or ARSA.
Security forces say the bodies are among about 100 Hindus missing since ARSA attacked at least 30 police outposts August 25.
There was no immediate way to independently verify the government's assertions.
The ARSA is the group whose raids on police posts in August triggered a military backlash that resulted in hundreds of thousands of Rohingya refugees fleeing for Bangladesh.
Rights groups say there is overwhelming evidence that the Army is using its crackdown on militants to systematically purge the 1.1-million strong stateless Rohingya from its borders, as per PTI.
More than 420,000 Rohingya Muslims have fled to Bangladesh since August 25.
Rohingyas, who trace their roots back generations in Myanmar, are a stateless minority who have mostly been stripped of their citizenship in the predominantly Buddhist country.