George Lyon made the claim in the closing speech at the Scottish Lib Dem conference in Aberdeen.
He rejected the Scottish Government position that membership can be sewn up in the 18 months between a Yes vote and formal independence from the UK.
Mr Lyon, campaigning for Lib Dem votes in the European election this May, said: "The question at these European elections is not simply in or out of the EU.
"The Scottish referendum means that the question Scots have to confront is do we want to be in Britain or out of Europe?"
He told party activists that the shortest time a new country has taken to become a full EU member since 1995 was eight years.
He argues that Scotland would be forced out of the EU and have to reapply for membership. The SNP says that Scotland, being part of the EU already, would be able to renegotiate from within the UK.
Questions remain about what terms Scotland would have to accept, with some suggesting the country would have to agree to adopt the euro or join the Schengen free-travel area.
The SNP argues that voting to stay in the UK means Scotland could be forced out of the EU if a future British government goes ahead with a proposed in/out referendum on Europe.
A spokesman for First Minister Alex Salmond said: "The only threat to Scotland's continued EU membership comes from Westminster's proposed in-out referendum and the Tory-led Government which George Lyon supports.
"A Yes vote in September will guarantee Scotland's future in Europe and ensure we have a voice and seat at the top table for the first time ever.
"Scotland is already part of the EU, so as an independent country will not be an accession state, and we will negotiate the specific terms of our continued membership from within."
A Yes Scotland spokesman said: "Scotland has been a member of the European Union for more than 40 years and our continued membership is in the best interest of all member states.
"The No campaign's continued scare tactic flies in the face of expert analysis, like that given by Graham Avery, honorary director general of the European Commission, confirming the EU will make it easy for an independent Scotland to continue membership after independence.
"The only threat to Scotland's continued EU membership comes from the UK Government's proposed in-out referendum that could drag us out of Europe against our wishes."