The 44-year-old was attacked by another inmate Rajesh, they said.
Officials declined to spell out details of the incident, including the reason for the attack, maintaining that an inquiry by prison authorities was on.
Perarivalan is being treated at the prison hospital, police said.
Rajiv Gandhi was killed by a suicide bomber at nearby Sriperumbudur on May 21, 1991 and seven persons-- Murugan, Santhan, Perarivalan, Nalini, Robert Payas, Jayakumar and Ravichandran -- were convicted in the case.
Nalini's death sentence was commuted to life in 2000 following a cabinet recommendation and appeal by Rajiv's wife Sonia Gandhi.
The Supreme Court had commuted the death sentence of Murugan, Santhan and Perarivalan in February 2014 following delay in deciding on their mercy plea.
The Tamil Nadu government had in March this year decided to remit the sentences of all the seven convicts.
However, the matter soon went to the Supreme Court and is pending there, with the Central government questioning the state's powers to grant remission to them on specific grounds.
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