Sturgeon said Britain's June referendum decision to leave the European Union meant semi-autonomous Scotland, which voted to stay in the bloc, could demand more powers from London over immigration.
"We are determined to maintain Scotland's current position in the European Single Market," she said in the introduction to a paper containing the proposals, entitled "Scotland's Place in Europe".
A "differentiated option" for Scotland, such as the rules that apply to non-EU members of the European Free Trade Association (EFTA) and the European Economic Area (EEA), could apply.
"The Scottish people did not vote for Brexit and a 'hard Brexit' would severely damage Scotland's economic, social and cultural interests," she said, adding that 80,000 Scottish jobs were at risk if Britain took the country out of the EU.
Iceland, Liechtenstein, Norway and Switzerland are in EFTA and the first three are also part of the EEA, which provides free movement of persons, goods, services and capital within the single market.
Sturgeon said that continuing the free movement of EU workers into Scotland would not mean the creation of a hard border with England if the rest of Britain instead chose to restrict immigration.
EU workers could be prevented from moving from Scotland to other parts of Britain by modifying immigration rules on employment and housing, she said.
Asked whether Britain could remain in the single market and customs union, she said: "We have to assume that is not the direction they will go".
She said she was not planning separate negotiations with the European Union but warned that if Scotland fails in its bid to retain EU ties "the option of independence must remain on the table".
A spokesman for Prime Minister Theresa May, who has promised to begin the formal procedure to leave the European Union by March 2017 at the latest, said London would "look closely" at Sturgeon's plans.
"The government is committed to getting a deal on exiting the EU that works for all parts of the UK -- which clearly includes Scotland -- and works for the UK as a whole," the spokesman said.
Sturgeon has put forward draft legislation for a new independence referendum to go before the Scottish parliament, even though the country voted in 2014 against breaking away.
The British government would have to give the final go-ahead for another independence vote, just as it did last time.