One Harvard study found that introverts’ brains work differently, and have thicker gray matter compared to extroverts. In people who are strongly extroverted, gray matter was consistently thinner. Introverts also showed more activity in the frontal lobes, where analysis and rational thought take place.
Another study that scanned brains of both introverts and extroverts found that, even in a relaxed state, the introverted brain was more active, with increased blood flow.
Regardless, I don’t think being an introvert or extrovert causes you to be smarter or not; I think it’s how often you interact with people. There are still other factors for IQ to be taken into account however.