The by-election is being held to fill the vacancy caused by the death of former chief minister Jayalalithaa.
The superstar said in a tweet, "My support is for no one in the coming election".
Rajinikanth's statement comes days after music composer and BJP candidate for the bypoll, Gangai Amaran, called on him.
Amaran's son Venkat Prabhu had tweeted on Sunday that the actor had wished him 'success' in his political innings during the brief meeting.
He had also posted a picture of his father with Rajinikanth at the latter's residence.
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