The branches in East Kilbride, Cumbernauld, Perth, Alloa and Stornoway – which employ in total almost 50 staff – may be moved as the company seeks partners for the controversial venture.
The Post Office, which could work with the likes of WH Smith, the Co-operative or other businesses, said the range of services would not be affected and branches could be open longer.
But there was dismay in the communities affected and from the Communication Workers Union (CWU), whose members are among the 49 staff affected.
It also raised fears of longer queues after similar problems at WH Smith-franchised post offices.
One of those affected, Stornoway, won the title of best performing branch last year.
Scottish Labour's Shadow Minister for Postal Affairs, Ian Murray MP, said: "People across Scotland really value their post offices and want to be able to access a range of services at them, crucially receiving appropriate advice and assistance.
"However, the announcement today raises huge concerns that certain services like motor vehicle licences, passport check and send services, bureau de change and travel insurance on demand will no longer be easily available to local people.
"The UK Government claims to have no planned closure programme, but this would seem to be closure and reduction of services by stealth.
"They must answer how the future of our cherished post offices is to be protected."
Gregg McClymont, Labour MP for Cumbernauld, Kilsyth and Kirkintilloch East and Shadow Pensions Minister, added: "I am seeking an urgent meeting with Post Office Ltd to discuss what this means for local people."
Angus MacNeil, the SNP MP for the Western Isles, called for officials to explain the development to local people, adding that following Stornoway's award, the "Post Office now seems to want to dismember it".
His SNP colleague for Perth and North Perthshire, Pete Wishart said: "This seriously undermines the credibility of the Post Office as a national service provider, treats staff abysmally and cloaks a restriction in services in the guise of improvements for the customer."
Keith Brown, SNP MSP for Alloa, said the local branch was well used. He added: "These plans potentially could see the service moved out of the town centre and could have serious consequences for Alloa."
Michael McCann, Labour MP for East Kilbride, Strathaven and Lesmahagow, said: "It is a public service and should continue to be so."
The CWU is seeking guarantees because rules over the transfer of employees' rights – known as Tupe – had not applied when the last tranche of Crown Post Offices were franchised and did not cover pension rights and pay increases.
General secretary Billy Hayes said a Consumer Focus report had criticised the performance of post offices franchised to WHSmith. They were the worst performer on queue times and scored badly on quality of service and accessibility, he added.
He said: "Post offices provide a dedicated specialist service to communities which will not be replicated by a window or two in a bigger shop. It leaves huge questions about the future of the Post Office."
The change relates to Crown Post Offices which are directly managed by Post Office Ltd. In total across the UK, 70 Crown Post Offices have been selected for franchising.