IS militants have been using the sprawling site as a command base since taking control of the city in May.
Some reports suggested Iraqi forces had retaken control of the complex.
The Iraqi military launched an operation this month to push IS out of Anbar province, large swathes of which are controlled by the militants.
The operation to retake the university complex was supported by US air strikes against IS positions around Ramadi.
A number of buildings in and around the complex were badly damaged or destroyed, Athal al-Fahdawi, a provincial councilman, told Associated Press.
The university is 5km (3 miles) south of Ramadi, which is the capital of Anbar province.
Recapturing the complex from IS would be a significant boost to the Iraqi forces’ efforts to reclaim the city.
Sabah al-Noamani, a spokesman for Iraq’s counter-terrorism forces, said the university was a “significant stronghold and a key command base” used by IS to co-ordinate attacks around Ramadi.
He said government forces were attempting to separate the university from nearby districts to cut supply routes for retreating militants.
IS seized parts of Ramadi, which is only 100km (60 miles) west of the capital Baghdad, along with the nearby city of Falluja and much of Anbar in January last year.
Iraqi Prime Minister Haider al-Abadi told the BBC in May that the city could be retaken from IS “in days” but the militants still control most of it.
Anbar province, which is predominantly Sunni, covers a vast stretch of the country west from Baghdad to the Syrian border, and contains key roads that link Iraq to both Syria and Jordan.