Police said the clash occurred following altercations between the AIADMK (Amma) and AIADMK (Puratchi Thalaivi Amma) groups during campaigning in a street in Ezhil Nagar.
One person each from the rival groups was seriously injured in the clash, police said, adding, the incident was recorded in a CCTV camera installed in a shop in the street.
While Ramalingam (60) of AIADMK (Puratchi Thalaivi Amma) group was admitted to Rajiv Gandhi Government Hospital, Nithyanandam (39) of the other group was admitted to a private hospital, police said.
The bypoll was necessitated due to the death of former Tamil Nadu Chief Minister J Jayalalithaa last year.
TTV Dinakaran is the candidate of AIADMK (AMMA).