In a Facebook post, Vijayan said the actress, who came to the filmdom as a child artist in Malayalam, had left behind a handful of unforgettable acting moments which her fans can cherish forever.
"The demise of Sridevi, known for her overwhelming presence in the Indian film world for the last five decades, was painful," he said.
The Chief Minister also said the sudden death of the actress, who immortalised several characters in different languages, was an "irreparable loss to the Indian film industry."
Sridevi had won the best child actress title in Malayalam for her performance in the film Poompatta (1971).
The actor (54) died late in the night reportedly due to cardiac arrest in Dubai, where she had gone to attend her nephew Mohit Marwah's wedding.