Barroso made the comments in an interview published in Italy's Corriere della Sera newspaper on Thursday.
Commenting on a controversy that has broken out most recently in Europe in Britain, Barroso was quoted as saying that he opposed laws that said what could and could not be worn.
"But there are matters of common sense," he said.
"I give you an example: a teacher who presents herself to students with a completely veiled face is not doing something reasonable in our society.
"And in general, if a person wants to communicate she can't present herself with a veil that covers her entire face, except for a small opening for the eyes. It's clear that that's an obstacle."
By making such comments, Barroso threw himself into the highly charged debate that has broken out in some European countries.
The controversy about veils in Europe was rekindled when Jack Straw, Britain's former foreign minister, said Muslim women who wore full veils made community relations difficult, calling veils a "visible statement of separation and difference".
"If a person wants to communicate she can't present herself with a veil that covers her entire face, except for a small opening for the eyes. It's clear that that's an obstacle"
Jose Manuel Barroso, the European Commission president
Tony Blair, the British prime minister, called veils a "mark of separation", while Romano Prodi, the Italian prime minister said it was a matter of common sense that people show their faces in public.
The question of whether Europe is doing enough to integrate Muslims has been addressed by the government since the attacks in July last year when British-born Muslim suicide bombers killed 52 people.
Turkey's EU bid
Barroso also reiterated worries about predominantly Muslim Turkey's progress towards EU membership, saying necessary reforms were proceeding very slowly.
"I'm sorry to say it, but things are going badly," he said.
"We're at a critical moment. The reforms in Turkey are proceeding very slowly and today I don't see the progress I would have hoped for.
"Let's hope that the Finnish presidency [of the EU] will manage to avoid a traumatic stop to negotiations. But, honestly, I am worried."
Barroso was referring to proposals from the Finnish EU presidency to resolve a dispute between Turkey and Cyprus threatening to derail Turkey's attempts to gain EU membership.