Twenty-nine fishermen and crew were on board the trawler Sea Merces MFR1125, when the incident happened Thursday mid-morning, more than 70 nautical miles off the coastline.
"Six people are still missing. Twenty-three sailors have been rescued, 12 of them were injured, and were sent to the Hospicio Hospital in Margao for treatment," a Goa marine police spokesperson said.
The rescue operation was conducted by the Indian Coast Guard and the Goa Police Marine unit, which brought to shore most of the sailors.
Rescue operations continue near the collision site, and a search is on for any remaining survivors.
An Indian Navy official said the trawler could have collided with a merchant ship, passing through the navigation channel off Goa.