According to Election Commission officials, 7.32 per cent voters have cast their ballots since polling began at 8 a.m.
The major contenders are AIADMK's E. Madhusudhanan, DMK's N. Marudhu Ganesh, Dinakaran -- contesting as an Independent -- and Bharatiya Janata Party's K. Nagarajan.
There were reports of malfunctioning of an electronic voting machine (EVM) at one polling booth, the officials said.
Over two lakh voters are eligible to decide the fate of 59 candidates in one of the smallest constituencies in Tamil Nadu.
The by-poll was necessitated following the death of AIADMK leader and Chief Minister Jayalalithaa on December 5, 2016, who represented the seat.
The counting of votes will take place on December 24.
Elaborate security arrangements have been made with around 15 companies of para-military forces and over 2,500 security personnel and several closed circuit television cameras, flying squads and static surveillance teams being deployed.
Although the poll was first scheduled to be held in April, it was cancelled due to complaints of large-scale voter bribing by a candidate.