RGU said a downturn in the regional economy due to the falling oil price had affected the university's income.
It also reported a reduction in demand for courses from students from oil-producing countries.
RGU said the aim was for the savings to be made through a voluntary redundancy scheme.
Prof Ferdinand von Prondzynski, principal of the university, said: "RGU will embark on a period of re-profiling its workforce to address the financial challenges and our strategic needs, allowing us to pursue ambitious targets for the successful, sustainable development of the university.
"We will continue to make a leading contribution to economic growth here and across Scotland, widening access to higher education, and the availability of high value knowledge and skills for the economy and society."
An additional £2m of savings are to be made via operational costs.
Aberdeen's Robert Gordon University (RGU) is to cut staff costs by £4m - meaning about 100 jobs are expected to be lost.