The accused, whose identity is yet to be established, has been arrested from Maharajganj in Uttar Pradesh, said Ravindra Yadav, Joint Commissioner of Police (Crime).
A call was received by Najeeb Ahmed's relatives three days back demanding Rs 20 lakh for his release, the officer said.
A Crime Branch team, under the supervision of DCP(Crime) G Ram Gopal Naik, traced the location of the man, who had allegedly made the call from his mobile phone and nabbed him, sources said.
However, the missing student's family denied receiving any such call.
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"We have not received any call demanding ransom," a member of Najeeb's family said.
Meanwhile, six students who were served notices seeking their consent for polygraph test, have still not agreed to it.
Najeeb's roommate, Mohd Qasim, has also not given his consent for the lie-detector test despite agreeing to it earlier.
Last year, in November, a guard at JNU's Mahi Mandavi Hostel where Najeeb was staying had received a letter which claimed that the missing student was being held captive in Aligarh. However, on investigation, the letter was found to be bogus.