Anbe Sivam begins with ad filmmaker Anbarasu (R. Madhavan), who prefers the much-abbreviated A. Aras rather than his full name, arriving at the Bhubaneswar Airport in Odisha, India. He is about to board a flight back to Chennai for his wedding. However, he learns at the airport that his flight has been cancelled. While waiting for further announcements, Aras watches the television news about a terrorist threat at an airport in Mumbai. Remarking to himself that the country is going to the dogs, he looks around and sees a bespectacled man with scars taking out something rolled up in a newspaper from his bag. Pictures of a pipe bomb shown among the items seized by the Mumbai police flash through his mind. He informs the authorities, only to learn that the man was simply taking out a cucumber.

The man, who is physically challenged, is Nallasivam a.k.a. Nalla (Kamal Haasan). Nalla introduces himself to Aras, and they get to know each other. However, Aras underestimates Nalla, ignoring his sage advice and friendly overtures, resulting in some comical events in the airport. Then, announcements are made that all flights have been canceled due to the inclement weather and Aras realizes he needs a room in a nearby hotel for the night. He is informed, much to his consternation, that the five-star hotel where he was staying before is now fully booked, leaving him optionless. Nallasivam helps him find a place in a two-star hotel nearby, where Nalla and Aras are forced to share the same room. Aras' resentment of Nalla makes him act selfishly in trying to get rid of Nalla; at every juncture, Nalla does him a favor which leaves Aras with a guilt-ridden heart. The next morning, Aras takes a taxi without waking Nalla to find his own way to Chennai. Aras realizes that the floods have blocked most of the roads and even the train station is flooded. He gets mugged by a man at the station who offers to help him with his luggage but instead steals all his money. Nalla comes to the statio