Mrs Singh has alleged that Pradeep Chauhan recorded her conversation with him on August 6 and then threatened to post it on social media unless he was paid Rs 2 crore.
Bharti Singh and union minister VK Singh dnaindia
She has also told the police that Chauhan has a licensed revolver and has threatened her family.
Police said they were still in the process of questioning Chauhan and no decision on his arrest has been taken.
Police sources claim that the suspect intended to splice her conversation to distort the content.
V K Singh retired as the chief of the Indian Army in 2012 and subsequently joined the BJP. He is one of two ministers of state for Foreign Affairs.