Speaking at the Barcelona Centre for International Affairs, Almunia stated that if a part of EU member state separates, "the segregated part is not an EU member."
The Commission's competition regulator Almunia also said the EU was "very concerned" about Catalonia's push for independence.
Almunia, a Spanish socialist politician, said Madrid and Catalonia now had to conduct "cool-headed" face-to-face talks on the Catalonia issue.
Half of all Catalans, or 49 percent, are in favour of independence for the region while just over a third, or 36 percent are against, according to a poll ran by centre-left daily El Pais earlier this month.
A huge protest on Catalonia's National Day on September 11th National Day saw hundreds of thousands of people link hands across hundreds of kilometres in support of independence for the region.