The current Italian government has introduced the "ministry of industry and made in Italy". That's what's it called, made in Italy, in English in the official name. I guess they're going to fine themselves.
"Fatto in Italia" would be just as good, but might not be as widely understood by non-Italian speakers.
It would feel weird to Italians too. Made in Italy is a sentence that has a long history and is widely used. Fatto in Italia would be laughed at. Then, if it becomes a law, it will be fatto in Italia. I bet against it.