A gang of five armed men stormed into a bank in Mapusa and held its staff and customers hostage at gunpoint before decamping with Rs 13 lakh cash on Friday.
People managed to catch two robbers, who were handed over to the police.
Chief Minister Manohar Parrikar has sought a detailed report from the police.
"A gang of five robbers entered the Indian Overseas Bank located in the heart of Mapusa city on Friday afternoon and attacked the manager, a clerk and a sweeper in the bank by taking the staff and customers hostage," a senior police official said.
The robbers were armed with pistols and knives and fired in the air before robbing the bank, he said.
"The belongings of the customers who were standing in the queue during the peak hours of the bank were also snatched away by them," the official added.
According to the official, while two of the robbers were caught by the people, three others managed to flee with Rs 13 lakh cash.
"The two robbers were caught 150 metres away from the bank and were badly beaten up by the people," he said.
Police said the accused have been admitted to a hospital.
"Right now their condition is such that they are not able to speak, which is why their statement is yet to be recorded," the police added.
The police are on the lookout for three other accused.