For HSPs who suffer from severe stress symptoms and overwhelm, an introvert personality can be vital for their health.
Because many define introversion as shyness and even self-centeredness, the HSP introvert personality can be misunderstood.
Overstimulation And The Introvert Personality
If your nervous system becomes overwhelmed easily, then withdrawal is a necessity, a matter of self preservation. Highly sensitive people cannot simply shut out intruding sensory irritants.
The HSP nature synthesizes and integrates information rather than excludes or compartmentalizes. As a result, HSPs often will develop an introvert personality to block out stimulus. A noisy party with loud music will not be a comfortable place for an HSP. Very high levels of office noise will be distracting and irritating on a long term basis.
Having an easily overaroused nervous system can cause a highly sensitive person to become more tentative and reluctant to pursue social situations. HSPs can often seem shy and withdrawn to those less sensitive and by the standards of the non-HSP they are.
If an HSP has experienced rejection in their early life of who they are, they will be guarded around other people, exacerbating their shyness. HSPs need the friendship of other HSPs, people who will understand and accept them, in order to handle the substantial rejection of sensitivity in our culture.
Men who are HSPs have a particularly difficult time living in an aggression prizing dominant culture.
Bullying, Abuse and the HSP Shyness
Many HSPs have experienced bullying for being different. HSPs can be easy targets because they are not only different but also less aggressively oriented than others. An HSP may also withdrawn to an introvert personality to manage social rejection, pressures to conform or other forms of negative social pressure.
If an HSP has the experience of bullying, or other forms of abuse when they were young, they are naturally going to be shy. HSPs have a hard time recovering from abuse, so their tendency to become shy can be self protective. If in addition to abuse, an HSP experiences a disregard for their suffering by the educational system or within the family, the trauma is then compounded leading to a feeling of devaluation. This situation raises the potential for long term depression if the situation is uncorrected over a long period of time.
HSPs can often seem shy and withdrawn to those less sensitive and by the standards of the non HSP they are. If an HSP has experienced rejection in their early life of who they are, they will be guarded around other people, exacerbating their shyness.
Being different is a major challenge. For an HSP, life can present so many land mines of potential harm that it can be very difficult to feel safe in the world. HSPs cannot change the world, but they can neutralize some of its negative effects, with planning, skill building and wise choices.
HSPs can be a paradox. On the one hand, they are often shy making them hard to get to know. On the other hand, their talent for observing nuances gives them an intimacy with a subject matter (or person) that can be unnerving for the non-HSP. Yet as Elaine Aron observes in her books about HSPs, while the highly sensitive person can be weak in areas prized by culture and need non-HSP support, non HSPs may not easily value the less quantifiable benefits of HSP talents developed because of their quiet, introvert nature. 
 Elaine N. Aron, Ph.D., The Highly Sensitive Person, (New York, Broadway Books, 1996) 17-18.