Merapi, about 280 miles east of Jakarta, the capital, has been spewing gas and lava for days, but activity increased on Tuesday, officials said.
Edi Purwanto, of the Mount Merapi evacuation post, said: "The lava has spread out in various directions. The lava domes are weakening.
"Since Monday we have evacuated ... more or less 2,000 people. The people that we need to evacuate are around 11,000."
About half of those would be moved in lorries over the next two days, he said.
Schools and government buildings are being used to house those displaced.
"It is no longer a mere call for the people to evacuate, they now have to evacuate, we are not taking any chances," said Agung, a local official.
Scientists at the volcano say that an eruption could occur at any time, particularly after the recent earthquake in the region last month which killed more than 6,000 people.
Volcanic experts say the quake may have weakened a large lava dome, the collapse of which could trigger a lethal cascade of lava and toxic gas.
"It is no longer a mere call for the people to evacuate, they now have to evacuate"
Mount Merapi last erupted in 1994, when the volcano released a gas cloud that burnt about 60 people to death.
Indonesia sits on the Pacific "ring of fire", named for its heavy volcanic and seismic activity.