Unidentified miscreants pelted stones at Aiyar's office in Mayiladuthurai, damaging some window panes, police said, adding security had been stepped up at the office.
Aiyar, presently a Rajya Sabha member, had earlier been elected to the Lok Sabha from Mayiladuthurai constituency.
At the AICC meet in New Delhi yesterday, Aiyar had said, "I promise you in 21st Century Narendra Modi will never become the Prime Minister of the country... But if he wants to distribute tea here, we will find a place for him," an apparent reference to his childhood days when he sold tea.
Aiyar's jibe instantly drew flak from various quarters including Jammu and Kashmir Chief Minister Omar Abdullah.
Around 50 BJP workers staged a 'tea-selling' demonstration outside TNCC headquarters Sathyamurthy Bhavan here, protesting against Aiyar's remarks. They were later detained by police.
At Kumbakonam, BJP members held a demonstration near Head Post Office and condemned the remarks made by the Rajya Sabha MP.