In a letter to LibDem Chief Secretary to the Treasury Danny Alexander, Oli Rehn said doing both would "not be possible".
Mr Alexander said the comments showed "an independent Scotland would face a simple choice - using the pound like Panama uses the dollar, or joining the EU: It can't have both."
No campaigners described Mr Rehn's intervention as "devastating".
But the Scottish Government accused anti-independence campaigners of scaremongering.
A spokesperson for Scottish Finance Secretary John Swinney said: "A week ago, the No campaign were claiming Scotland would have to join the Euro, now they are saying we wouldn't even get into the EU - they should at least try and keep their scaremongering consistent".
In his letter, Mr Rehn suggested that using the pound without a currency union - so-called sterlingisation - would create a significant stumbling block to EU membership, the lack of a central bank.
Mr Rehn wrote: "As to the question whether 'sterlingisation' were compatible with EU membership, the answer is that this would simply not be possible, since that would obviously imply a situation where the candidate country concerned would not have a monetary authority of its own and thus no necessary instruments of the EMU."
He also said he believed that both Scotland and the EU would be "stronger" if Scots reject independence later this month.
Aides to Mr Swinney attempted to bat away central bank concerns. "EU membership requires that you have to have financial institutions such as a monetary institute," one said, "which is contained within our proposals."
SNP leader Alex Salmond has hinted that Scotland could pursue sterlingisation if the remaining UK refuses to enter into a currency union with an independent Scotland.
The First Minister insists that the opposition of the main pro-Union parties to his plan is a "bluff".
But pressed on what he would do if there was no "sterling zone", Mr Salmond has repeatedly said that Scotland could not be prevented from using the pound.
"Sterlingisation" is akin to the more common phenomenon of "dollarisation", in which countries far from American shores use the US dollar.
Critics warn drawbacks include no central bank, which would normally act as a lender of last resort if commercial banks got into trouble, and no control over things like interest rates.
Mr Rehn stood down as the European Commissioner for Economic and Monetary Affairs earlier this year.
The Finnish politician had previously served as the commissioner for EU enlargement.
In a speech to the Chatham House think tank last night, Mr Alexander said: "The nationalists say that they will be able to continue using the UK pound even if they become a separate state.
"Because, even if the rest of the UK doesn't agree to a currency union, they have said that Scotland would use the pound without a formal agreement."
"This is an arrangement known as 'sterlingisation', which would mean Scotland would not have a central bank to set interest rates or act as a lender of last resort.
"This is not only a bonkers idea which flies in the face of any reasonable notion of what independence means and which would impose costs and risks on people and businesses in Scotland ... it is also incompatible with Scotland's smooth re-entry into the EU."
Last night pro-independence sources questioned whether Mr Alexander had broken strict "purdah" rules prohibiting the use of Government resources to campaign by revealing the correspondence.
Both Edinburgh and London governments have agreed to respect the weeks around the independence referendum.
The Treasury insisted that there had been no breach because Mr Alexander's letter to Mr Rehn had been sent from his MP's office the not the Treasury.