Such a person would be asexual or nonsexual, their condition would be called asexuality or nonsexuality:
Asexuality (or nonsexuality) is the lack of sexual attraction to anyone, or low or absent interest in sexual activity.
There is also a website about it (it seems google takes its definition from there), but I cannot reach it to check from behind my current firewall. If google does take it from there, this page says:
An asexual is someone who does not experience sexual attraction. Unlike celibacy, which people choose, asexuality is an intrinsic part of who we are. There is considerable diversity among the asexual community; each asexual person experiences things like relationships, attraction, and arousal somewhat differently.