Introverts are not necessarily curmudgeons. I like people. I need people. But people wear me out. I used to substitute teach some, and having significant interactions with 150 people in a single day left me exhausted and crabby. I wanted to crawl into a dark room and muffle the door. The difference between introverts and extroverts is a matter of how people affect their energy level. When an extrovert (say, Bill Clinton) is tired, he wants to go to a party to recharge his batteries. An introvert is discharging his batteries all the time he's with people -- even people he loves to be with; to recharge his batteries, an introvert has to get some alone time.
I use my introverted nature in my ministry. Because I am very comfortable in my head, I am able to understand things about my own thoughts and feelings that others may not understand about themselves. Because I am very verbal, I can describe or explain things going on inside people (drawing on my own inner experience as a first example) that other people are surprised but find helpful to hear. My self-awareness and education make me a sympathetic and perceptive counselor, as well as a preacher who gets right to the point (I tend to expose and dissect the heart instead of telling warm fuzzy stories). I have had to learn that the experiences I know best (mine) are not universal, but I understand fully what C.S. Lewis was talking about when he said that whenever he spoke about his own struggles and sins, it tended to strike home with his listeners.
In order to survive in a line of work that involves people, people, people, though, I have to take care of myself. I have to get enough rest. I have to schedule in alone time. I have to be able to read and think. I can't do one meeting right after another all day long; and indeed, the beauty of my entrepreneurial style of work is that I am in charge of my schedule. I can go from the intense encounter of ICU or a nursing home to quiet time in the woods to nice, dull paperwork, to a committee meeting, to a no-special-reason call. There is a rhythm to my day, and I can (usually) control how much stimulation is coming at me.
The one thing that introverts have to be especially aware of, though, is that you really have to make the effort to offer yourself to people. You have to be really present to this person, not trying to get some distance, or thinking about the next thing. I've also had to learn that I don't have all the answers -- and that having an answer is not necessarily important. Being there is important. Being there in crisis, in illness -- offering a hug, NOT trying to explain WHY bad things happen -- this is how one shows love. I tell those who cry out, "Why did God . . .?" that even if we could understand Why, it wouldn't make it hurt any less. The only answer to "Why?" is "I love you." The guy who lives in his head has to learn how to show love in other than verbal forms, in order to make that point and act as a conduit by which God can make that point.
I've always said that it doesn't matter what skills and experiences you bring into ministry, God will use them. You don't have to worry about not having skills that somebody else has (say, playing a musical instrument). I've used my fantasy game background, my scouting experiences, even my odder hobbies and so on. God brings people into my path who can use what I have to offer. No part of the minister's past or personality is without use. That said, introverts as well as extroverts can make good and successful ministers.