The actor met him in a hotel near the airport soon after Modi arrived from Salem by helicopter. Details of the meeting were, however, were not known, BJP sources said.
The BJP leader is to address a rally here.
The sources claimed the meeting would have a positive impact on the younger generation voters for whom Vijay is the 'hearthrob'.
They said the 'Vijay Fans Association' is already involved in various social and welfare activities and the meeting, particularly the photographs taken, could play a major role in the election, particularly among women voters.
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Modi was scheduled to meet the actor in Chennai after meeting Rajnikanth on Sunday last but the latter was busy shooting in Andhra Pradesh and could not make it, they said.
VIjay has tweeted that he was privileged to be invited to a "non-political" meeting with Modi. "I am looking forward to meeting him," he posted on Twitter.
Modi shared the dais with Vijayakanth, another popular actor and leader of DMDK, an NDA ally, during electioneering in Salem, about 200 km from here.
Rajinikant had said he was a "well-wisher" of Modi and wished him "all the best" while Modi had described the superstar as a "good friend".