At her monthly press conference at Bute House, Ms Sturgeon said a summer referendum would not give the public enough time to become familiar with the arguments surrounding the issue.
Ms Sturgeon said she was “reasonably confident” Scotland would vote to stay in the EU, but was now “less sure” about a Yes vote being secured in the rest of the UK.
She also advised those campaigning to stay in Europe to adopt a different approach from the Better Together campaign, which was accused by Nationalists of negative campaigning in 2014.
According to the First Minister, opinion polls were “starting to look less than comfortable”.
Ms Sturgeon said: “I am increasingly concerned by reports and they are just reports, that the EU referendum could be held as early as June if there is agreement struck at the European Council in February. My concern is if that is the case it would leave barely four months – including the period of the Scottish election – for the public to fully engage in and for the arguments about EU membership to be heard fully.
“My fear is that by focussing on the narrow issues up for renegotiation the UK government is in danger of selling the pass on the big economic and social arguments for staying in the EU and then leaving too little time for these issues to be engaged with.”
Ms Sturgeon added: The thing about the Scottish referendum and the issues are not identical, but the two campaigns there started quite far apart and ended up fairly close in the end analysis. Here the two campaigns are much much closer. My fear is that if the In campaign runs the same kind of campaign as the No campaign in the Scottish referendum, they could find themselves overtaken. David Cameron needs to get away from the very narrow focus on these renegotiation issues and make the big picture case for staying in.”