The miners are trapped in the Beaconsfield Gold Mine, about 20 kilometres north-west of the city of Launceston.
Australian Prime Minister John Howard has offered his support for the three miners, with the Tasmanian government admitting there are grave fears for their safety.
A remote-controlled front-end loader is being sent into the mine in a bid to rescue them.
Beaconsfield Gold Mine manager Matthew Gill said 17 miners were underground at the time of the rock fall, but 14 managed to escape unharmed.
Mr Gill said it is not known whether the three men had survived the rock fall.
Rescue teams have been unable to make contact with the men and fallen rocks have prevented rescuers from reaching them.
The remote-controlled front-end loader would be fitted with a camera and used to excavate the fallen rocks, Mr Gill said.
Geoscience Australia confirmed that a minor earthquake, of 2.1 magnitude, occurred in the area of the mine collapse.
West Tamar Deputy Mayor Max Burr said the tight-knit community is deeply upset by the event.
"(It's) absolutely horrendous, there will be a lot of concern, not only in Beaconsfield, but all around Tasmania everywhere," Mr Burr told AAP.
"It is a major concern and all you can do is feel for the families and the miners who are down and hope they're okay. Certainly there would be a lot of ... angst in the local community because whoever they are, they would be well known within the local community.
"I am quite hopeful that the community will be hoping and praying that the people get out all right, that would be the immediate response. I am quite sure there would be a lot of optimism they can get out alright."
Beaconsfield has a population of about 1,000 people and the mine is the town's largest employer, providing jobs for about 300.
Mr Burr said it is the first incident at the century-old mine since it reopened in the early 1990s.
Earlier, West Tamar Mayor Barry Easther said the council is doing all it could to organise support for the miners' families.
"It's a devastating time in the local community," he told the Channel Nine television Network.
"We all live on hope, but it's a bad rock fall. Thankfully the other miners who were underground at the time have come to the surface safely. We have to brace ourselves as a community for and pull together."