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.
The leak has sparked a statewide alert, as fuel is drifting at a speed of around three kilometres per hour and could soon impact the ecologically sensitive Kerala coastline.
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.
Some containers were carrying dangerous substances such as calcium carbide, a chemical that reacts with seawater to release highly flammable acetylene gas, officials said.
The ICG is leading pollution response efforts and monitoring the spread of the oil slick. PTI TGB ADB