Generally, no.  Acupuncture needles are tiny.  They are solid, not hollow like the hypodermic needles used to give injections, and they are much, much thinner – usually not much greater in diameter than a human hair.  While you may occasionally feel a very mild prick as a needle is first inserted, the sensation that follows should not be painful.  It is variably described as deep, heavy, pulling or distending, and it may be localized to one spot or may radiate away from the point of origin.  Most people find acupuncture extremely relaxing, and many fall asleep during treatment.