Witnesses say several youths assaulted the sociology teacher with sharp weapons in front of Bihashpalli when he was returning home around 3pm Saturday.
He sustained severe injuries on his head and shoulder.
Islam, 48, later started for a hospital on a rickshaw but fell down when it approached Binodpur near the campus.
Bystanders rushed him to the Rajshahi Medical College and Hospital (RMCH).
"He died as soon as he was taken to the operation theatre around 4pm," Dr Mamtaz told bdnews24.com.
The motive behind the attack is not clear yet.
The RU Teachers' Association has also announced to boycott classes and exams on Sunday.
In 2006, RU geology teacher S Taher was murdered at his home on the campus.
A court sentenced Taher’s colleague Mia Md Mohiuddin, caretaker Jahangir Alam, and two others -- Abdus Salam and Najmul -- to death over the killing.
The High Court later commuted death sentences of Salam and Najmul but upheld maximum penalty for Mohiuddin and Alam.