It also asks for Edinburgh's principal, Peter Mathieson, to be called before Holyrood.
Writing in The Times, David Farrier, a professor of literature and the environment, said: "Staff morale is lower than ever, eroded by job insecurity, gendered and racial disparities in pay and unsustainable workloads.
"Students' education suffers when lecturers have to worry about paying the rent.
"Meanwhile, university leaders fixate on driving through unjustified pension cuts that will see members of the Universities Superannuation Scheme (USS) lose on average more than a third of their retirement income."
He said higher education institutions face a choice between "a future in which our universities remain among the best in the world or one in which only those with a private income can afford to pursue an academic career".
The letter, which was sent to Education Secretary Shirley- Anne Somerville and Jamie Hepburn, the higher education minister, states: "We are deeply concerned about the future of higher education in Scotland.
"We request that [you] look into this matter, and that the education, children and young people committee holds a full inquiry into how Scotland's universities are managed, and how staff and student confidence can be restored.
"We also ask the Scottish Parliament to call Edinburgh's principal, Peter Mathieson, to appear before parliament to explain why there is no end in sight to this crisis."
A spokeswoman for Edinburgh University said it was listening to concerns around the USS pension scheme.
She said: "As one of 340 institutions who offer the scheme to their staff, we are limited in what we can do on these nationally negotiated issues.
"While we take every opportunity to make our views clear, we are one voice among many."
She added: "We are not complacent and are committed to securing a long-term outcome for the USS pension that is fair, affordable and sustainable for both individuals and employers.
"Where we can, we have implemented a number of initiatives to address aspects of employment conditions for our staff.
"We have been a voluntary living wage employer since 2012 and we have not used zero-hour contracts since 2014.
"We have doubled investment in our annual staff reward scheme to recognise the contributions of more staff.
"We are committed to a fair offering for staff and offer many generous staff benefits, including excellent flexible working and family friendly policies.
"We know that this ongoing situation has caused significant disruption and concern for our students, and we will continue to do everything we can to ensure that the impact on learning and teaching is minimised."
A Scottish Government spokeswoman said it had "no direct role in determining whether any parliamentary committee should undertake any inquiry into the pay and pensions of those who work in universities".
She added: "Central to our Fair Work approach is the expectation that employers, workers and trade unions work together to reach the right decisions and ensure workers are treated fairly."