The First Minister demanded the moratorium so Scots can have their own say on what do with the public "asset" in the event of a Yes vote next September.
"The Scottish Government is firmly opposed to the privatisation of Royal Mail and this proposed sell-off of an essential public service should be subject to a moratorium until the result of Scotland's referendum is known," he said. "Privatisation is a deeply flawed decision with potentially serious and long-term effects on Scotland's rural communities and rural economy."
Most Scottish MPs opposed the sell-off in a vote, which he said proves decisions should be taken independently. "I am therefore calling on the Prime Minister to put a halt to this deeply misguided action until the people of Scotland have had their say on Scotland's future next year," he said.
"The Royal Mail is a profit-making enterprise with massive public assets which are as much the people of Scotland's as they are the rest of the UK's. As a result, it is unacceptable for those assets to be sold off before the people are able to make their decision on Scotland's future.
"The Royal Mail should be in public hands and following independence we will ensure that the people of Scotland have the opportunity to keep it that way."
Members of the public can apply for shares as well as institutional investors. Analysts expect the sell-off to raise up to £3 billion.
Scottish Liberal Democrat leader Willie Rennie said the UK Government's scheme will not affect the universal service.
A Royal Mail spokeswoman said: "Private investment will allow Royal Mail to grow our parcels business. This in turn will help us to continue to deliver the Universal Postal Service. The Postal Services Act 2011 sets out very clearly the minimum requirements of the Universal Service. They will continue to apply after any sale."