According to the CDC:
"Gloves are not required when administering vaccinations, unless persons administering vaccinations are likely to come into contact with potentially infectious body fluids or have open lesions on their hands." [link]As such, the practice of wearing gloves is left up to the discretion of the person administering the shot.
Some offices/hospitals may have a policy in place that makes it mandatory, but technically it is not required.
Of course, many individuals will point out a conflicting policy based on "Universal Precautions" which can potentially be interpreted as mandatory use of barrier protection (like gloves) whenever there is the possibility of bloodborne pathogen transference (which some may interpret as risk is always present).
However, if one actually reads the Universal Precautions put out by the CDC as it relates to blood drawing (considered higher risk than immunizations),
"In universal precautions, all blood is assumed to be potentially infective for bloodborne pathogens, but in certain settings (e.g., volunteer blood-donation centers) the prevalence of infection with some bloodborne pathogens (e.g., HIV, HBV) is known to be very low. Some institutions have relaxed recommendations for using gloves for phlebotomy procedures by skilled phlebotomists in settings where the prevalence of bloodborne pathogens is known to be very low. Institutions that judge that routine gloving for all phlebotomies is not necessary should periodically reevaluate their policy. Gloves should always be available to health-care workers who wish to use them for phlebotomy." [link]Not quite the "mandatory" use of gloves some people stipulate when quoting Universal Precautions policy.
General Recommendations on Immunization. CDC 2/8/02
Perspectives in Disease Prevention and Health Promotion Update: Universal Precautions for Prevention of Transmission of Human Immunodeficiency Virus, Hepatitis B Virus, and Other Bloodborne Pathogens in Health-Care Settings. CDC 6/24/88