Coastal police said that some containers have been found along the southern Kollam coast.
The total number of containers washed ashore is not yet known, and authorities are working to manage the situation, they said.
Police have been deployed in all affected areas.
Reports indicate that at least four containers have been spotted so far along the coast of Kollam district.
Officials have urged the public to stay away from the containers, warning that the ship had 13 hazardous cargos among its 640 containers.
The cargo ship capsized and sank early Sunday, leading to a significant oil spill.
According to the Indian Coast Guard (ICG), the sunken vessel had 84.44 metric tonnes of diesel and 367.1 metric tonnes of furnace oil in its tanks.
The ICG is leading pollution response efforts and monitoring the spread of the oil slick.