He called for the current Safe Harbour deal, which allows the transfer of data to US firms, to be scrapped.
Facebook has not commented on the case.
At a hearing in Luxembourg on Tuesday the European Court of Justice's (ECJ) Advocate General said he would give his final opinion on 24 June - the ECJ will make its final decision thereafter.
Privacy principlesThe result of the proceedings could have wide implications for all US firms dealing with Europeans' data, including the likes of Twitter, Google, Microsoft and Yahoo.
It centres around the Safe Harbour agreement, in place since 2000, which allows US firms to collect data on their European users as long as certain principles around storage and security are upheld.
It means user data gathered in Europe can easily be stored legally in data centres within the US.
Those principles include giving adequate notice to users that their data is being collected, and suitable transparency over how it can be accessed and by whom.
The ECJ is considering whether the Safe Harbour agreement is effective in the wake of the Snowden leaks.
Mr Snowden alleged that Facebook and others were complicit in Prism, a surveillance system launched in 2007 by the US National Security Agency (NSA).
Euro dataA complaint against Facebook - which bases its European headquarters in Dublin, Ireland - was filed by Mr Schrems last year.
He said the network should be investigated over the alleged co-operation with US intelligence agencies in handing over user data from Europeans.
Mr Schrems said Facebook had acted against the Safe Harbour rules, and that local regulators should step in to protect Europeans' data.
The Irish Data Protection Commission (IDPC) said it would not investigate the claims, a decision that was challenged by Mr Schrems in the Irish High Court.
Judge Duncan Hogan then referred the wider matter of whether Safe Harbour was effective to the ECJ.
'Serious effects'The ECJ's eventual decision could have a dramatic impact on the business practices of Facebook and other US firms.
Scrapping the Safe Harbour agreement would make it much more difficult to transfer data from Europe to the US to be stored in data centres.
While Facebook has not made a formal statement on the case, the BBC understands that the firm would be likely to welcome updating the Safe Harbour rules in light of the Snowden revelations.
Some companies, such as Twitter, have said they would need to build new data centres in Europe to handle information, needlessly duplicating resources they already have in the US.
According to the Wall Street Journal