The petrol bombs were thrown in the wee hours of Tuesday at post offices located in Mylapore and Mandaveli.
The activists want India to boycott the Commonwealth Heads of Government Meeting (CHOGM) to be held at Colombo next month.
According to police, no person was injured in the attack, except for slight damage to the building wall and an air conditioner.
Following the attack, police beefed up security at central government offices and installations across the state. The Sri Lankan mission office here has also been provided additional security.