This recent study seems to show that reading fiction is strongly correlated with high levels of empathy, social understanding, and awareness. On the other hand, there is no similar connection between social skills and reading nonfiction.
Of course, as the authors point out, it is not clear which way the causation goes. It may well be that highly empathetic people tend to read more fiction, not that reading fiction makes you more empathetic. Personally, I hope that it's the latter effect that dominates; I need to justify my reading habits!
A related question: What about the the correlation between social skills and the ratio of fiction books read relative to nonfiction? For example, I probably read much more fiction than the average person, but I also read far more nonfiction than fiction. Does the ratio of fiction to nonfiction say more about my empathy or lack thereof, or is it the absolute amount of fiction read that is decisive?