The deadly storm has killed seven people in neighbouring Sri Lanka and affected the lives of almost 20,000 people.
The Tamil Nadu government today requested the Centre to deploy helicopters of the Indian Navy and Coast Guard for the search and rescue of missing fishermen, mostly from Kanyakumari, in the wake of cyclone Ockhi.
Almost 9,000 people have sought shelter in relief camps.
Cyclone Ockhi to recurve towards Gujarat coast: Top developments
Weather experts warned of more heavy rains to come, as the water level rose in several rivers in southern India.
Rescue operations were underway, with the Indian navy, air force and coast guard searching for dozens of fishermen unaccounted for in the Thiruvananthapuram-Kollam coastal area, said the New Delhi Television news channel.
The Brihanmumbai Municipal Corporation's disaster management unit advised people against visiting beaches after a high tide alert was issued for Monday and Tuesday, ANI reported.
Thousands of people are in Sri Lankan relief camps amid widespread destruction of property.
The Kerala state emergency department said almost 3,200 people were in relief camps.
More than 2,000 people have taken shelter in relief centers in Kanyakumari and Tirunelveli districts in Tamil Nadu state and in Lakshadweep, a group of 36 islands, officials said.
India's eastern coast - including major cities like Chennai and Bhubaneswar - are prone to storms that wreak vast damage between April and December.
The depression is likely to further move towards Tamil Nadu and south Andhra Pradesh in the next three to four days, the India Meteorological Department (IMD) said on Saturday.
This was conveyed to Prime Minister Narendra Modi by Chief Minister K Palaniswami during a telephone conversation between the two leaders last night, a state government release said.