The incident took place yesterday afternoon and people managed to catch two of the robbers, who were handed over to the police.
Chief Minister Manohar Parrikar has sought a detailed inquiry report from the police into the incident.
"A gang of five robbers entered the Indian Overseas Bank located in the heart of Mapusa city yesterday afternoon and attacked the manager, a clerk and a sweeper in the bank by taking the staff and the customers hostage," a senior police official 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.
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According to the official, while two of the robbers were caught by the people while they were trying to escape, three others managed to flee with Rs 13 lakh cash from the bank.
Police said that the accused duo has 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," police said.
Police are on the lookout for three other accused.
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