Melbourne University Associate Professor Allison Milner, 36, was crushed by a 106-year-old elm tree that fell on her in Princes Park at Parkville about 8.30am on Monday.

Firefighters pulled her from beneath the tree and she was taken to the Royal Melbourne Hospital in a critical condition but died soon after.

"She was a dear friend of mine, colleague and she was an incredibly bright woman by any stretch," her close friend Professor Anne Kavanagh told The Age.

"Allison's tragic death is a great shock and an immense loss to the university community," Professor Terry Nolan, head of the university's School of Population and Global Health, said on Monday night. "Her research spanned the fields of suicide prevention, work, gender and disability."

The City of Melbourne has said the 1913 tree had been inspected on July 12 this year as part of an annual inspection of the row of trees.

"The inspection last month did not highlight any signs the tree posed an increased public safety risk," the City of Melbourne said in a statement.

The tree has since been removed for further inspection by both the City of Melbourne and an independent arborist. The council is also examining other trees in the area.

The tragedy follows on the heels of wild weather in the state, with Melbourne battered by strong winds and heavy rains.

It is the second such tragedy in three days. A large tree fell on a family's car at Fernshaw, in the Yarra Ranges, on Friday, killing a woman.

Australian Associated Press