The alleged pirates, along with some crew members being held hostage, were on board a Thai fishing vessel that had been hijacked up to six months ago off the coast of Somalia.
It is thought to have since been used as a floating base to mount attacks on shipping, a ministry statement said.
Mumbai police were expecting to interview all those detained when they arrive in the city.
The navy and coastguard were sent to hunt the pirates after the crew of a Greek-flagged vessel said they had been attacked some 100 nautical miles west of Kavaratti, in Kerala.
Two high-speed skiffs were located in the early hours of Sunday and chased back to the mothership. Coastguard and navy were fired on twice, the statement said, and a brief shootout followed before the pirates surrendered.
Fifteen alleged pirates -12 Somalis, two Ethiopians and a Kenyan - face trial in India after they were caught in the same area on 28 January.
They were also said to have used another hijacked Thai fishing vessel as a mothership.