Asaduzzaman Khan Kamal made the revelation speaking to reporters on Sunday, a day after senior journalist Shafik Rehman's arrest in a case related to the plot.
The minister refuted the BNP allegation that Rehman was arrested for writing against the government.
"He has been arrested on specific charges," he said.
The case was lodged against the BNP’s US unit leader Mohammad Ullah Mamun.
His son Rizve Ahmed Caesar, FBI Special Agent Robert Lustyik, and another US citizen, Johannes Thaler, have been sentenced to several terms in jail in the US over the plot.
In the verdict against Caesar, the US court said the convict had bribed Lustyik to get information to harm a 'prominent' Bangladesh national. Thaler conducted the deal.
Court documents did not mention a name, but described the victim as 'son of the Prime Minister of Bangladesh and an advisor to the Prime Minister on information technology.'
It said that Caesar admitted that he intended to 'scare,' 'kidnap' and 'hurt' Joy.
Documents submitted to the court of the Southern District of New York also say that Ceaser gave the information to a 'journalist in Bangladesh' and 'obtained in return approximately $30,000.'
Now police have arrested Rehman in the case filed over the plot with Ramna police station.
The home minister said two to three persons, including Rehman, had communication with those involved in the conspiracy in the US.
"Of them, we suspect Shafik Rehman maintains communication with them.
"That's why he has been arrested for questioning," the minister said.
About the others, he said, "You may know one of them, a newspaper editor. He is now in jail."
"You'll know when the time comes," Kamal said about the other person.
Police's counter terrorism unit chief Monirul Islam told bdnews24.com that Amar Desh acting editor Mahmudur Rahman, in jail in a number of cases over violence, will also be shown arrested in the case over the plot to abduct and murder Joy.