The protesters, who have set up six camps at the site, say the Letpadaung mine near the town of Monywa is causing environmental, social and health problems.
The protest is the latest example of increased activism by citizens since an elected government took over last year following almost five decades of repressive military rule.
State television broadcast an announcement ordering protesters to leave or face legal action.
The mine is a venture between a Chinese firm and a company controlled by Burma's military.
"We strongly condemn last night's order from the Home Ministry," said Thwe Thwe Win, one of the protest leaders.
She added: "We will not stop our protest until our demands are met."
Protesters say they want the mining project to be totally halted and any concessions made publicly in front of the media.
This protest, which began in August, poses a direct challenge to the army because of its financial interest in the mine.