The two leaders held a 45 minute discussion in Brussels this morning. Mr Barnier also met with the Labour leader Jeremy Corbyn and Welsh First Minister Carwyn Jones.
"This was a useful and constructive meeting and I welcomed the opportunity to discuss Scotland’s priorities with Mr Barnier - in particular our view that the UK should seek to remain in the single market," Ms Sturgeon said afterwards.
“I outlined to Mr Barnier that our priority is to protect Scotland’s vital economic interests, and that the Scottish Government will do all it can to build a consensus against an extreme Brexit outside the single market, which would have potentially catastrophic consequences for jobs, investment and our living standards."
Mr Barnier has stressed he will only negotiate with the UK Government.
"We have always been clear that this is not about holding separate Scottish negotiations – it is for the UK as the member state to negotiate with the EU – and as such we will continue to work hard to influence the UK position. However, meetings like this are helpful in developing a mutual understanding between the Scottish Government and the EU as these vital negotiations gather pace."
Mr Barnier said Britain must offer more clarity on its position on the ''divorce bill'' financial settlement with the EU - as well as the status of expat citizens and the nature of the future border with the Republic of Ireland - if it is to make progress towards a deal on trade arrangements after Brexit.
Scottish Labour's Europe spokesman Lewis Macdonald MSP said: “Unlike the Tories, Labour wants a jobs-first Brexit that will prioritise the economy, jobs and living standards - and that is what Jeremy Corbyn will outline when he meets Mr Barnier.
“Nicola Sturgeon should join this fight for a fair Brexit rather than simply using this process to agitate for independence.”