No. Introversion is the low end of extraversion, a preference for quieter settings, smaller company and time alone; shyness is tension and inhibition around other people, especially strangers. A person can be either, both or neither, and the two are only modestly related.
The evidence
Cheek and Buss (1981) built separate scales for shyness and for sociability and found them only modestly correlated: knowing that someone had little appetite for company told you little about whether they felt awkward in it. They then watched pairs of strangers talk. The people who were both shy and sociable, who wanted company but feared it, talked least and showed the most tension; the unsociable people who were not shy were content with less. Ashton, Lee and Paunonen (2002) asked what the centre of extraversion is and found social attention, the enjoyment of being noticed and engaged with, rather than any absence of fear. Low extraversion is a low appetite, not a high fear.
Where each one sits in the Big Five
The twenty-item introvert or extrovert test and the extraversion scale of the 120-item test ask about talking, taking charge, keeping busy, seeking excitement and feeling cheerful. None of the six facets of extraversion is shyness. The discomfort side of shyness, the self-consciousness that makes a person embarrassed or awkward in company, is a facet of neuroticism in the 120-item test, not of extraversion. That is why a shy person can score anywhere on extraversion: a shy extravert wants the room and dreads walking into it, and a confident introvert goes, enjoys it for an hour and leaves.
What a low score does not mean
A low extraversion score does not mean fear of people, and it does not mean poor social skill. It does not mean wanting to be left alone always, only recovering alone. And a high score does not mean the absence of shyness: a sociable person can dread first meetings and still seek them out.
What it means for your results
If your extraversion score is low and company does not make you tense, the score is describing a preference. If company makes you tense and you still want it, that is the shy and sociable pattern Cheek and Buss described, and an extraversion score alone will not show it; the self-consciousness facet under neuroticism in the 120-item test is the closer measure. Read the score as how much company you seek, not how you feel once you are in it.
The introvert or extrovert test takes three minutes and places you on the single scale. The Big Five test adds the six facets of extraversion and the self-consciousness facet beside them.