Commission spokesman Margaritis Schinas said the “Barroso doctrine” continued to apply.
Former commission president Jose Manuel Barroso set out the legal view that if one part of an EU country became an independent state it would have to apply for EU membership.
At a briefing in Brussels, Mr Schinas said: “The commission does not comment on issues that pertain to the internal legal and constitutional order of our member states.”
But he added: “The Barroso doctrine, would that apply? Yes that would apply, obviously.”
Meanwhile, the secretary-general of Nato Jens Stoltenberg said an independent Scotland would have to gain the approval of all 28 allies before it could join the alliance as a new country.
Speaking in Brussels yesterday, he said Scotland voting to leave the UK would mean it also had to leave the defence bloc.
Mr Stoltenberg said: “If it happens, then the UK will continue as a member of Nato but a new independent state has to apply for membership and then it is up to 28 allies to decide whether we have a new member.
“All decisions in Nato are taken by consensus, so we need the consensus of all allies. By leaving the UK it will also be leaving Nato.”