The job losses will affect staff at the Institute's Aberdeen, Dundee and Edinburgh sites.
Prospect negotiator Ian Perth said: "This will come as devastating news to scientists and support staff at the institution.
"We are very disappointed that the funding arrangements for the Institute mean that the employer deems this necessary.
"In 2016, staff made a £1.7m annual contribution to the organisation’s finances by agreeing to significant pension changes and leaving the civil service defined benefit scheme.
"Prospect’s priority is to seek to protect our members from compulsory redundancy and to ensure that all those who remain in the Institute will remain on a sustainable basis.
"We have held initial discussions with the management team and have been offering robust feedback on their proposals so far.
"From our initial engagement, it is clear that the employer will make significant efforts to ensure that any redundancies are voluntary.
"We welcome the employer’s decision to initially open a voluntary register and to offer enhanced redundancy terms for those who are attracted by voluntary exit," Perth concluded.
The institution, which is primarily funded by the Scottish Government to carry out research on its behalf, has suffered significant budget cuts in recent years.