"Around 6.30 AM, 15 people who were stranded on board the vessel were safely rescued by the Coast Guard", Chennai Port Trust officials told PTI.
Search involving the Navy and Coast Guard is on for the missing six persons, the officials said.
The vessel 'Pratibha Cauvery' with 37 crew on board ran aground near Elliott's Beach in South Chennai, about 200 metres away from the shore.
One crew member drowned after a life boat carrying him and his 21 colleagues capsized in choppy waters while 15 others were rescued with the help of several agencies including Navy and local fishermen yesterday.
The ship belonged to Mumbai-based Pratibha Shipping Company.
Two persons were killed in Tamil Nadu as Nilam crossed the coast between Tamil Nadu and Andhra Pradesh border yesterday without causing much damage.