Anything to be worried about? Probably not. However, you might want to search the term "selective mutism" which is a severe social anxiety disorder in which stressful environments can render a child mute (in addition to other behaviours). The main difference between shyness and selective mutism is function. If her shyness is hindering her life in ways as eating, sleeping, communicating, etc., then you might want to see a specialist dealing with anxiety disorders. By the way, the earlier the diagnosis and thus treatment, the better the prognosis.
More likely than not your dtr. has an introverted temperment. If this is the case this is something she inherited the way one inherits red hair or brown eyes. Introverted kids and adults have a rich inner world. They tend to be quiet and may take awhile to warm up to social situations. They tend to make a few very good friendships as oppossed to having a large network of friends, and acquaintences. They are often quite sensitive and think deeply. They tend to prefer being alone or in the company of close friends and family members. Many intellectually gifted persons are introverts. Today, there are several good books about introverted children. I am an introverted adult. I wish I understood my own introversion many years ago. Its taken me most of my lifetime to be comfortable with it. Please, check out one of these books. Also, good information about introversion can be found on the internet. Best wishes...