Yes, it can be done. You can be introverted and a good DM simultaneously. You just have to take a somewhat different approach.
I've been DMming for... well... a long time. The first time I ran a D&D game George Bush was president. No, not George W. Bush... His father. Yeah. I've been doing this a while...
...and doing it wrong.
If you're introverted you know how hard it can be to have sustained participation in a group of people. It's exhausting, frustrating, you get grumpy, tired, player characters start dying...
Believe it or not, there are ways to mitigate these problems so that you can be an awesome Dungeon Master AND an introvert. These are all things I've learned through experience, which means I did it wrong for a long time before figuring out how to do it right.
Keep your D&D group size small. Don't try to be the hero DM with 10 players because you hate to say no to anybody who wants to join. Sometimes you just have to say no. It stinks, but there may be other ways to handle it, like splitting into separate groups if you can get someone else to DM, or running both groups yourself on separate days. Don't feel beholden to the "always room for one more" idea. The best size for a D&D group if you're an introverted DM is 4 people. 5 is pushing it, 6 is the extreme upper limit that should probably only happen when someone occasionally wants to sit in for a session or two.
Keep the session relatively short. If you start to feel your energy level flagging and you find yourself daydreaming about retreating to your introvert den, that's a good time to call it a night on the session. For me, I find this is usually around the 3 hour mark but your mileage may vary. Plan for that number, once you know what it is. My players are used to getting to my house between 7 and 8, then leaving around 11.
Take some time in your introvert den before the game begins to charge your batteries and get ready. If you work all day and then immediately go into DM mode then you'll truly be torturing yourself. Set aside at least an hour or so between the time you get home and the time people start arriving. This is even more important for men, because psychologically, men need more wind down time after work than women do.
Gently but firmly encourage people to hit the road when the session is over. This usually isn't too hard if your session ends late at night, but sometimes people get into chatterbox mode because your D&D session might be the only time they see each other. Just let them know you're tired and it's nothing personal, you're just ready to get some rest. You aren't being a jerk if you do this and you're not lying either. Your emotional/mental batteries are depleted and you need some time to recover.
To be honest, I'd give this advice to ANY DM, but it's critical for introverts. We live in a culture that rewards and promotes extroverted behavior, so we usually think in terms of what an extrovert would do. That needs to change.