My son entered daycare when he was 14 months old and until he reached the age of kindergarten, he was in a new daycare each year. His needs changed and the daycare and/or staff didn't have what he needed.
Despite being around a lot of children at a very young age, he was a very shy kid. So am I, but my mom pushed me hard toward things that I was not comfortable doing.
So, in each new environment my son and I would enter into, we stepped to the side and surveyed the action. I would say things like, "looks like there are a group of kids playing with puzzles over there", or "can you see the kids playing on the swings? Looks like they're having fun. What do you think?" I would allow him time to look things over and decide for himself his level of involvement. There wasn't any pressure to join in.
In addition, he had great male role models at my job who taught him wonderful ways of greeting people. Walk right up, hand outstretched, "Hi I'm Matt, I'm pleased to meet you" and shake their hand firmly, looking them right in the eye. Practice this over and over again.
Kids today don't get that practice of greeting people and making small talk. So they get very anxious because they don't know what to do. I'm believing that a lot of social anxiety can be helped with regular practice talking to people you don't know. Standing in line at the grocery store? Say, "wow, it's certainly a hot day out there today, isn't it?"
I'm shy as a rule, but I make myself engage with people just to keep in practice so I don't freak out. You might try this with your daughter and also ask her what makes her so anxious about her encounters to give you clues to help her.