Reports say a crowd attacked a bus in Rakhine province after blaming some of the passengers for the gang rape and murder of a Buddhist woman.
In another incident, at least 10 people were injured in the state capital Sittwe when police broke up a protest.
It is the worst violence to hit the province in recent months.
Sectarian and ethnic tension persists in the country despite a new, supposedly tolerant climate introduced by the civilian-led government which came into power 15 months ago.
The bus attack took place near the town of Taungup in Rakhine province, which borders Bangladesh, on Sunday evening, police and residents said.
It was thought to be carried out by mostly Buddhist ethnic Rakhine people.
"More than 100 people beat and killed those people," a resident told AFP news agency. "The residents even torched the bus."
The reason for the attack is unclear, but some residents say it was a revenge attack following the rape and murder of a Buddhist girl in another part of the province last month.
But the Burmese Muslim Association said most of those killed were Muslims visiting a mosque from central Burma.
That account was corroborated by unnamed residents quoted by Reuters news agency, who said those killed were not from the area.
No arrests have been made. A police investigation is under way.
In another, apparently unrelated incident at least 10 people were injured after police fired rubber bullets at a mob who attacked their police station in Sittwe, reports said.
A 13-year-old protester was among those injured, witnesses said.
There were contradictory reports about what triggered the protest, but some accounts suggested anti-Muslim sentiment could have played a part.
Rakhine is home to Burma's largest concentration of Muslims, including much-persecuted Rohingya Muslims, and their presence is often deeply resented by the majority Buddhist population.
In a joint statement quoted by Reuters, eight Rohingya rights groups based outside Burma condemned the attack on the Muslims on the bus, whom they termed "Muslim pilgrims".
Although it appears those on the bus were not Rohingyas, the groups said the attack followed months of anti-Rohingya propaganda stirred up by "extremists and xenophobes".
Buddhist residents in western Burma have killed at least nine Muslims as sectarian tension worsens in the region, police say.