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'
Earlier, Islam said Siddique's killer or killers might have been jihadis.
"We believe Islamic militants were behind the attack, because the nature of the incident is similar to previous attacks carried out on atheist writers and activists," he said.
"Siddique was very active organizing cultural events in the university," 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 police commissioner sounded a cautionary note, saying 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."
CNN's Elizabeth Johnson and Don Melvin contributed to this report.