The detainee is a member of the banned Jamaat-ul-Mujahideen Bangladesh (JMB) who killed Rajshahi University's professor Rezaul Karim Siddiquee, Xinhua news agency reported.
Criminals slit the professor's throat on April 23 while he was waiting for a bus near his residence, the police said.
Siddiquee, also a writer and cultural activist, died on the spot. "We've arrested one JMB man who directly took part in the murder," said the official.
A number of secularist writers, bloggers and publishers in Bangladesh were killed or seriously injured in attacks perpetrated by Islamist extremists since 2013.
Militants have claimed responsibility for the past murders.
JMB, campaigning for establishment of Islamic rule in Bangladesh, carried out a series of bombings in the country.
Hundreds of JMB leaders and activists were rounded up while six top leaders of the group, including Shaikh Abdur Rahman, were hanged in 2007.