According to sources, the four individuals were detained by the Special Task Force of the Lucknow Police from Gorakhpur and Rae Bareli.
Ranjiyt Bachchan was shot dead on Sunday morning by unknown gunmen in Lucknow while he was on a morning walk.
Police sources said that the suspects were detained on the basis of call details of the deceased's mobile phone.
One of the suspects had made a call to a close relative of the Hindu leader, minutes after Ranjit Bachchan was shot dead.
The police are investigating all possible angles in the murder case and are likely to question Ranjit Bachchan's second wife, Smriti.
A property dealer from Gorakhpur is also on the police list for interrogation.
Ranjit Bachchan was shot at in the head multiple times by bike-borne assailants on February 1 in broad daylight. The incident took place near the Global Park in Hazratganj area.
The attackers fled from the spot after the firing.
Bachchan was immediately rushed to Lucknow Trauma Centre where he was declared brought dead.
His younger brother Aditya, who was with him at the time of the incident, also suffered bullet injuries.
Four police officials, including two PRV police personnel, a constable and an outpost in-charge were suspended after the murder.
The police also released CCTV footage of the murder suspect and announced a reward of Rs 50,000 for any information about any suspects' whereabouts.
Notably, this is the second incident when the leader of an ultra-right fringe Hindu outfit has been killed.
In October last year, leader of the Hindu Samaj Party and former member of the Hindu Mahasabha, Kamlesh Tiwari, was shot dead by unidentified assailants in the Naka area of Lucknow.
( With inputs from IANS )