Up to 25% of musicians have stage fright (performance anxiety), according to one study (Barbar et al., 2014). So stage fright is a common problem with musicians. The good news is that there are effective treatments available to help with stage fright.
Performance anxiety in Brazilian musicians: prevalence and association with psychopathology indicators. Barbar AE, de Souza Crippa JA, de Lima Osório F. J Affect Disord. 2014 Jan;152-154:381-6. doi: 10.1016/j.jad.2013.09.041.