At some point there was a movement to intern Italians who had never formally renounced their citizenship, regardless of how long they'd been in America. There were some arrests, mostly in California. Interestingly, Joe DiMaggio's parents were Italian citizens living in the US, and he raised a huge outcry.

From the New England Historical Society site (http://www.newenglandhistoricalsociety.com/in-the-hidden-history-of-wwii-italian-enemy-aliens-were-interned-restricted/):

Attorney General Francis Biddle, in his book Brief Authority, described how he told Roosevelt about plans to intern enemy aliens. “And you're going to intern all of them?" said the President in a tone that suggested he approved of the idea. "Well, not quite," replied Biddle. "I don't care about the Italians," continued Roosevelt. "They are a lot of opera singers, but the Germans are different; they may be dangerous."

And anecdotally, my grandma was a young Italian immigrant in Brooklyn during the war and remembers Italian-run stores putting up signs asking their Italian customers to exclusively speak English inside, or denouncing Mussolini. A lot of the very poor, Southern Italian community were initially strong supporters of Italian fascism and had to fight very strongly to prove their loyalty after the US entered the war. My grandmother and her family never tried to hide their heritage (it was way too obvious) but they were definitely pressured to overemphasize their patriotism.

Some sources!:

http://articles.latimes.com/2010/aug/23/local/la-me-italians-20100823

http://www.archives.gov/research/immigration/enemy-aliens-overview.html

http://www.sfgate.com/magazine/article/A-SECRET-HISTORY-The-harassment-of-Italians-2866287.php