Not the EU as an institution but single countries. I wouldn't be surprised if Austria closes their border if there are more cases in Northern Italy. Germany, Switzerland and France could also follow. I believe they'd still let freight through (maybe with tests for drivers) to not hurt the economy too much. Ironically, the refugee situation a few years back helped those countries as they now have the infrastructure to patrol borders better and built centers that could as well be used to isolate potentially infected people.

But I also wouldn't count on all of this happening too fast, there's still passenger flights arriving from mainland China in Europe.