HMP Barlinnie is approximately 500 people above its capacity and is at the "biggest risk of failure", according to Audit Scotland, which would put the whole prison system in jeopardy.
Warning that there is no strategy for accommodating inmates if HMP Barlinnie becomes uninhabitable, Holyrood's Public Audit Committee urged the Scottish Government and Scottish Prison Service (SPS) to develop "robust contingency plans" as their top priority.
An investigation into the prison system by MSPs found that Scotland's jails are deteriorating due to "10 years of capital underspend" to balance the books in the face of Government cuts, which it said are undermining the rehabilitation of convicts.
It is claimed a replacement for HMP Barlinnie in the Glasgow area will be built by 2025 but the committee's report states that work is "likely" to overrun, adding: "The impact of the delay in the capital programme cannot be over-estimated."
Committee convener Jenny Marra said: "Audit Scotland says HMP Barlinnie presents the 'biggest risk of failure in the prison system' but warns there is no clear contingency plan for accommodating the 1,460 prisoners it currently holds should it fail.
"Developing a contingency plan for Barlinnie in the event that it fails must be of the highest priority.
"Given the state of prisons generally, the Scottish Government and the SPS must develop robust contingency plans should any other part of the prison estate become uninhabitable."
Overcrowding in Scottish prisons, with many inmates forced to share cells designed for just one person, is "undermining the Scottish Government's policy objectives of rehabilitating prisoners and reducing reoffending", the report states.
MSPs are calling for the SPS "to be funded for the prisoner population that it currently holds and for the expected increase", arguing there is "no evidence" that prisoner numbers will fall in the short term.
The SPS has managed to remain within its budget allocation over the last 10 years due to repeated underspending on capital projects such as upkeep of buildings, leaving parts of the prison estate at risk of becoming unsuitable for housing inmates.
The report found that the SPS has been hit by a 12.5% real-terms reduction in its revenue budget, while capital programmes for HMPs Barlinnie, Inverness and Greenock are all behind schedule.
Justice Secretary Humza Yousaf said there are contingency plans in place for Barlinnie but they are not anticipating a "catastrophic failure" at the jail.
He told BBC Good Morning Scotland: "For every single part of the prison estate we have a contingency plan, for example if there were to be some kind of catastrophic failure.
"We would move them partly across the estate but there may be other solutions that we would also have to look at as well, but nobody is anticipating a catastrophic failure at Barlinnie.
"What we're anticipating is investment going into the current estate, including Barlinnie, building the new Barlinnie and of course working with the prison estate to see what other further improvements can be made.
"But of course, ultimately, if we reduce the prison population we ease the pressure on Barlinnie, we ease the pressure right across the estate."
He also said: "The most immediate thing, and the biggest priority for us, is to reduce the prison population and, thankfully, through the presumption against short sentences and other measures we've taken, we're starting to see that decline."
A Scottish Prison Service spokesman said: "The Scottish Prison Service (SPS) welcomes the committee's report and will reflect on its findings.
"The safety and well-being of those living and working in our prisons is a priority for the SPS and it is to the credit of our staff that good order is maintained across our estate.
"It is well documented that the SPS is managing an increased prison population who have challenging and complex needs.
"The recent budget announcement by the Scottish Government acknowledges the significant challenges the service faces, particularly in response to population numbers, and our settlement for 2020-21 has increased in recognition of these pressures."