The SITE monitoring service reported the claim on Friday, citing a statement posted by the group online.
Ansar al-Islam, the Bangladesh division of al Qaeda in the Indian Subcontinent (AQIS), said its members had carried out the attack as "vengeance" because Nazim had “abused God, the Prophet Mohammad and Islam in Facebook posts”.
Reuters was not immediately able to verify the authenticity of the message but SITE said the group had provided a link to its digital signature to verify it.
The postgraduate law student was attacked as he was returning from a class at Jagannath University, police said.
"This operation was conducted to teach a lesson to the blasphemers of this land whose poisonous tongues are constantly abusing Allah, the religion of Islam and the Messenger," the AQIS message in Bengali and English read, according to SITE.
Al Qaeda leader Ayman al Zawahri announced the formation of AQIS in 2014 in a video posted online in which he said the group would spread Islamic rule and "raise the flag of jihad" across the subcontinent.