A 42-year-old man, Dinesan, was arrested in connection with the defacing of Mahatma Gandhi statue in Kannur district of Kerala, police said.
Police said he was mentally unsound and later released on bail.
Gandhi's bust near the Thaliparamba taluk office was found defaced in the morning with its spectacle carving damaged and a garland on it seen lying nearby.
Meanwhile, at a residential locality in Chennai, a bust of Dalit icon B R Ambedkar was found with paint smeared on its face and head.
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Police assured the agitated local people that action would be taken against the culprits.
"Based on a complaint from the local people, we have registered an FIR and two special teams have been formed to trace the culprits," Deputy Police Commissioner G Shashank Sai said.
More police pickets have been posted in the area for maintenance of law and order, he said.
A series of incidents of desecration of statues of various leaders, including Ambedkar, rationalist E V Ramasamy "Periyar" and Jana Sangh founder Syama Prasad Mookerjee, have been reported from different parts of the country over the past few days.
The incidents in Tamil Nadu were triggered after BJP leader H Raja had in a Facebook comment indicated that Periyar's statue would meet the fate as that of Lenin's statue.
However, facing flak from political parties in the state, he later deleted the post and blamed his social media administrator for the lapse.
He also expressed regret for the comment.
Meanwhile, superstar Rajinikanth today described as 'barbaric' Raja's comment but said the issue need not be 'magnified' further as the BJP leader expressed regret.