Speaking to reporters in Tiruvarur, Stalin said brokers from Tamil Nadu as well as other states are involved in this crime.
He said if justice is to be obtained, the probe should be done by the CBI.
Currently, the case is being investigated by the Crime Branch Crime Investigation Department of Tamil Nadu police.
To date, police have arrested four father-son duos for allegedly hiring proxies for write the entrance exam.
The police are also probing to see whether Mohammed Shafi, father of Irfan, is a quack.
The scam came to light when the Dean of the Government Medical College in Theni got two e-mails from a person, Ashok Krishnan, complaining against a first year student K.V. Udit Surya.
According to the complaint, Surya had failed twice in the NEET. He had cleared the recent exam opting for Mumbai as the exam centre, where a proxy wrote the entrance exam.
The college authorities found two different photographs.
Later, the police arrested Surya and his doctor father Venkatesan, working in the Government Stanley Hospital and an agent in Kerala for hiring a proxy to write the entrance exam.
While interrogating Surya and Venkatesan, police learned that there were several other first year medical college students who had engaged proxies for a huge fee - upwards of Rs 20 lakh - to write the exams.
According to police, Surya, Irfan, Praveen of SRM Medical College, and Rahul of Balaji Medical College have been detained for inquiry.
Police said the original photos in the hall ticket were substituted with that of the proxies while all other details remained the same.
( With inputs from IANS )