I don't have any children yet, but several nieces and nephews, and more pertinent, was very much like your son, and know why.
My parents are introverted. I didn't learn through observation or practice that EVERY person is an opportunity for an interaction. That idle conversation is enjoyable.
Things your son has probably seen you do:
Etc...ad infinitum
It sucks for you, but you are going to have to go out of your way to meet and talk to people, handle all your business with confidence, and more importantly, show that it makes you feel good and at ease.
It should go without saying that your son needs to feel valuable, powerful, and comfortable too. My parents and siblings handled everything, so I was slow developing on my own. Let him handle as many interactions concerning himself as you can. Has he ever bought anything at a store? Ordered his own food? It is difficult to look somebody in the eyes when you don't feel confident, competent, or valuable.
I was recently at a sporting goods store with my nephew getting t-ball supplies. My nephew tried on gloves, talked with the salesman, knew his cleat size, and when he was ready my brother absentmindedly handed him $80 and told him to go check out while we looked at the golf clubs (10 steps from the register). Another kid came in with her mom. The kid didn't do anything. The mom put a glove or two on her, picked up a pair of cleats and pants in her size, and then they marched to the front, where I'm sure she silently swiped her card. Granted, they were in and out in 10 minutes while we spent almost an hour. Obviously we can't accurately predict which kid is going to be more sociable when they are teens or whatever, but I would make a bet.