Injection site pain can indeed be a side effect of the HPV vaccine. Although by no means will everyone experience it, it is the most commonly reported of the HPV vaccine side effects. Almost 20% of people receiving the vaccine report injection site pain, and the actual prevalence of at least some discomfort at the site is probably somewhat higher.
I experienced this type of discomfort first-hand when I received the first shot of the Gardasil vaccine series. I could actually feel the injection as it went into my arm. It was painful -- not horribly so, but noticeably. Fortunately, my arm stopped hurting within 15 minutes of getting the HPV vaccine.
Personally I found injection pain, as one of the HPV vaccine side effects, to be no big deal, but it is useful to know that it's a possibility to expect if you're headed to your doctor's office for the vaccine.
Tucker, ME (2007)"Injection Site Pain Is Top Adverse Event for Gardasil" Skin & Allergy News 38(4):8