Authorities earlier said the student had been arrested but later clarified their report.
"We haven't arrested him or brought any charges against him yet," Rajshahi police Commissioner Mohammad Shamsuddin said Sunday. "He is a suspect, and we've taken him to our custody for interrogation."
The slain professor, 58-year-old Rezaul Karim Siddique, taught English at Rajshahi University.
He was waiting for a bus to take him to campus Saturday when he was attacked from behind and stabbed in the neck, police said.
It's unclear whether the attack was related to the recent hacking deaths
of bloggers in Bangladesh.
"He was neither a blogger nor an anti-Islamic campaigner, but the pattern of the murder indicates Islamist militants involved in the recent spate of killings of secular bloggers might have a link," Shamsuddin said.
ISIS claims responsibility
ISIS claimed responsibility for the killing, according to Amaq, the terror group's media agency.
"ISIS fighters assassinated a university professor for calling to atheism in the city of Rajshahi in Bangladesh," a statement from the group said.
CNN cannot immediately confirm ISIS' claim or its statement on the religious beliefs of the victim.
This month, Bangladesh Law and Justice Minister Anisul Huq said it was "safe to say that there is no existence of ISIS in this country."
Huq also dismissed reports "about the claim of ISIS that they're trying to make Bangladesh their base headquarter for operations in India, Bangladesh and Myanmar."
"That's their claim; one can claim anything," he said.
Village is a 'hotbed of militants'
Siddique "was very active organizing cultural events in the university," Deputy Police Commissioner Nahidul Islam said. "He was also planning to open a music school in his home village, Bagmara."
The village "is a hotbed of JMB militants," police said, using the abbreviation for Jama'atul Mujahideen Bangladesh, a fundamentalist Islamic organization.
But the deputy commissioner said police had not found evidence that the professor wrote or spoke against Islam.
'He had no political links'
And Anima Choudhury, a former student who studied literature with the professor from 2010 to 2015, said she saw nothing political in him that could have led to such an attack.
"I don't know what the motive is, but he was a very good person, and he had no political links," Choudhury said.
"He wasn't involved in any issues that can cause this. It's really mysterious, and it was really shocking, because we didn't expect something like this could happen to him. I guess we have to wait for the reasons."