The sociology teacher was struck with sharp weapons by several youths in front of Bihashpalli when he was on his way home on Saturday afternoon.
He suffered grave injuries on his head and shoulder, and died at the Rajshahi Medical College and Hospital.
The group's Facebook page, which was opened around five hours after the murder, says: "Our Mujahideens (fighters) executed a 'Murtad' (apostate) today in Rajshahi who had prohibited female students in his department to wear 'Burka' (veil)."
The page shows a picture of the slain teacher with a red X-mark on it. Below it is written in Bangla: "AKM Shafiul Islam (file closed)/ Offence: Apr, 2010/ Punishment: Nov, 2014."
Ansar al-Islam, an Islamist militant outfit, began operating in Iraq and Syria, where the 'Shariah'-based Islamic State is active.
Another Facebook page styled 'Ansar al-Islam' in Bangla found on the social media, was opened on Sep 9 this year.
Meanwhile, the Facebook page of 'Ansar al Islam Bangladesh-2' was opened around 8pm on Saturday.
RU teacher Islam, 48, was hacked around 3pm and was declared dead by the doctors an hour later.
Meanwhile, the Detective Branch (DB) of the Dhaka Metropolitan Police is yet to confirm whether Ansar al-Islam Bangladesh at all exists.
"We do not know of any organisation by this name. But new outfits are emerging now and then. So the existence of Ansar al-Islam Bangladesh cannot be ruled out," a DB deputy commissioner, working on militant outfits, told bdnews24.com on condition of anonymity.