"Maskawat Hasan Sakib alias Abdullah admitted his links to Rezaul Karim's murder and gave his confessional statement at the Metropolitan Magistrate's Court yesterday," Rajshahi's police commissioner, Mohammad Shamsuddin said.
Shamsuddin said police will hold a press conference to give more details on the investigation progress later today.
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Outlawed JMB has carried out a series of bomb attacks across Bangladesh, killing scores of people including two judges, prompting a massive anti-militant campaign.
Media reports earlier said police arrested Sakib from northwestern Bogra town in connection with the April 23 murder of Karim, an English literature professor of state-run Rajshahi University who was known for his love for music.
Suspected Islamists hacked him to death using machetes near his house in the northwestern city.
Karim was the second professor of the same university to be killed in nearly identical manner in past two years.
US-based private SITE Intelligence Group said the Islamic State claimed the killing.
"ISIS' Amaq Agency reported the group's responsibility for killing Rajshahi University professor Rezaul Karim for "calling to atheism" in Bangladesh," it had said in a tweet.
Bangladesh, however, ruled out existence of foreign Islamists outfits like ISIS and alleged that fundamentalist Jamaat-e-Islami was patronising the killing spree to portray the country as an abode of foreign militants.
Police visibly intensified investigations into a series of attacks on secularists and liberal intellectuals, bloggers and minorities including gay activists against the backdrop of growing criticism for failure to track down the assailants.
In the past two days police arrested three Rohingya Muslims, who took refuge in Bangladesh in view of reported persecution by authorities in neighbouring Myanmar, for their alleged involvement in the murder of a Buddhist monk in southwestern Badarban hill district last week.
The assailants slaughtered 70-year-old Buddhist monk Mawng Shoi Wuu, chief of the monastery located in the isolated and rugged Naikkhangchari area of Bandarban hill district.
Police on Sunday arrested 37-year-old Shariful Islam alias Shihab from Kushtia over the killing of the country's first gay magazine editor and his friend.
Police identified him as a member of outlawed Ansarullah Bangla Team, which according to the Site Intelligence Group was the Bangladesh affiliate of Al-Qaeda in the Indian Subcontinent (AQIS).
Xulhaz Mannan, 35, editor of a gay magazine, and a 25-year-old fellow activist Mahbub Tonoy were hacked to death in an apartment here on April 25 by up to seven attackers carrying machetes and guns.
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