All the four arrested persons are suspected to be directly involved in the murder, they said.
Police said that the four are being brought to Chennai from Bangalore, but did not elaborate further.
Hindu Munnani Tiruvallur District President Suresh Kumar was attacked by unidentified assailants at his photocopy shop in suburban Ambattur late in the night on June 18. He was rushed to a private hospital in a critical condition where he died without responding to treatment.