Police said at least 50 people were buried when a portion of the three-story building in Canacona fell, the Times of India reported.
One official said 11 bodies have been removed so far. However, "there are at least a dozen or more trapped under the debris," the official said.
Police, health and fire service personnel were using heavy equipment, gas cutters and a crane to reach trapped workers, the Times said.
Chief Minister Manohar Parrikar said the army was called to help with relief and rescue work.
A real estate development firm based Mumbai was handling the construction, the Times said.
Parrikar said police have been asked to work quickly to determine who was responsible for the accident.
"An FIR [First Information Report] has been filed against the builder, contractor and the municipal engineer in charge. We will not spare anyone," Parrikar said.