Khin San Hlaing, a lawmaker from the National League for Democracy party, said the confrontation at the Letpadaung copper-mine project occurred as police and Chinese workers erected a fence on land that the villagers claimed as theirs.
She said a woman in her 50s was fatally shot in the head, though it was not clear whether she was shot by police or mining company security personnel. Another woman was shot in the thigh, she said.
The massive project, a joint venture between a Myanmar military-controlled holding company and China's Wanbao Mining Copper Ltd., drew international attention two years ago when police forcefully dispersed protesters, injuring more than 100 Buddhist monks.
Many suffered severe burns from smoke bombs that contained white phosphorus, a substance not generally used to contain civil unrest.
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The mine has been the scene of some of the fiercest opposition to corporate land-grabbing in Myanmar since elected President Thein Sein came to power in 2011.
They worry that the mine is causing environmental, social and health problems.
Because of the outcry, work at the mine was temporarily halted. The mining contract was renegotiated to ensure that millions of dollars go toward community development projects and to pay compensation to villagers, allowing the resumption of mining activities.
Although the company has paid compensation to some villagers, others refused to take the money and insisted that they would hold on to their land.
"The police started firing with their guns and the Chinese security beat up the villagers on that land with axes and hammers, which injured a lot of farmers this afternoon," he said.