The panic was sparked by rumours that seismologist Raffaele Bendandi, who died in 1979, predicted the city would be devastated by a quake on 11 May.
Officials have insisted quakes cannot be predicted and special programmes have run on state TV calling for calm.
Experts also say there is no evidence Bendandi even made the prediction.
But many people said they were leaving the city to be on the safe side.
There are reports of an 18% increase in the number of city employees