The scroll was in the university library but had been mislabelled, a professor at the university says.It was previously thought the scroll was no more that a few hundred years old.
However, after carbon dating tests, the university has said the text may have been written more than 850 years ago.
The university's Professor of Hebrew Mauro Perani says this would make it the oldest complete text of the Torah known to exist, and an object of extraordinary worth.
The university says that in 1889 one of its librarians, Leonello Modona, had examined the scroll and dated it to the 17th Century.
However, when Prof Perani recently re-examined the scroll, he realised the script used was that of the oriental Babylonian tradition, meaning that the scroll must be extremely old.
Another reason for the dating is that the text has many features forbidden in later copies under rules laid down by the scholar Maimonides in the 12th Century, the university says.