Alex Neil questioned whether Scotland’s 15 regional health boards all need to have their own finance directors and HR departments.
He was speaking after Auditor General for Scotland Caroline Gardner warned MSPs it is a “challenge” for the NHS to recruit and retain staff.
Recent reports from the public spending watchdog highlighted concerns about NHS Tayside and NHS Highlands - with leadership challenges amongst the issues raised.
Ms Gardner said: “We are seeing it increasingly difficult not just to retain, but to recruit, to attract people to these jobs.”
The Auditor General said this is partly “because the jobs themselves are getting harder”, but also that “here in Scotland we do tend to pay less for those roles than the NHS in England does, which can make it difficult to recruit people externally”.
Mr Neil, who was health secretary for two years after taking over the job from Nicola Sturgeon in 2012, told the Public Audit Committee that a common theme in Audit Scotland reports on the NHS is “managerial weaknesses at every level”.
The MSP added: “Has the time not come for a fairly fundamental review, at national level, of all aspects of the management of National Health Service in Scotland?
“We have 22 NHS boards, 15 of them covering territorial areas, including Highland and Tayside. Do we need 15 directors of finance in this day and age of the computer? Do we need 15 HR departments?
“This is a huge overhead. If we could save in that huge administrative overhead, it would free up some resource to go into medical and healthcare provision.
“Is it not time for a very fundamental look at the whole structure?
“If we don’t modernise the model of delivery we could be sitting here having these same conversations, in fact the situation might be even worse.”
Ms Gardner told him: “The structure of the NHS is a matter for Government rather than me as Auditor General.”
But she added: “I do think that having the number of bodies that we do makes it harder to recruit, retain, develop the number of really high calibre people to do the jobs that are required.
“Running a health board is difficult in any circumstances but at a time when financial pressures are acute, and when we really do need to see that transformation to meet the needs of an ageing population, we need to make sure we are making the best use of the people with the skills and experience and capacity to do that.”
Meanwhile, the chief executive of Scottish Care is warning “we need to get serious” about providing care at the launch of a new report highlighting the critical role of care homes.
Dr Donald Macaskill will deliver the message at the national Care Home Conference in Glasgow today, where the ‘Essential care: the critical role of care homes’ report will be unveiled.
He will say: “A Scotland that invests in its people invests in care.
“The care sector is a people sector.
“It is also a sector that contributes massively to the Scottish economy - more than Agriculture, forestry and fishing and many other sectors.
“So why is it that we have so little focus on the need to invest in and grow the care sector?
“Why does it feel like businesses that care - that employ thousands of people, that are economic engines and care centres at the heart of our villages and towns - continually feel as if they are having to beg new resource, scrimp and save and be apologetic for asking for more?
“We need to get serious.
“We either want a world leading care sector with the best possible rights-based care or we want just enough, the sufficient, the it’ll just have to do approach.
“If we are serious about being a country that cares, then let’s grow the sector, let’s invest time, energy and resource in being the best; let’s change the record from it costing too much to contributing so much; let’s invest to ensure survival and sustainability, growth and cutting edge innovation; let’s invest in care by creating a special economic task force to make social care an economic priority.”