A senior district police official said the two vandalised a bust-size statue of Ramasasmy in an inebriated state.
Police identified the arrested as Muthuraman and Francis.
While Muthuraman is suspected to be a BJP worker, Francis is believed to be a CPI activist, police said.
The incident comes against the backdrop of a row over comments made by BJP leader H Raja indicating that statues of "Periyar" could be the next to be pulled down after a Lenin statue was razed in Tripura.
BJP's state unit distanced itself from the issue, saying it was his personal view.
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