I don't know of a canonical reason, but there are real physiological reasons that support the idea for the character
Several studies have found pain is as unique as the individual. An American Pain Society study discovered differences in patient biological, psychological and sociocultural factors can cause vast differences in post-operative pain. A New Zealand study found cultural differences influenced pain perception between study participants. Other studies reinforce findings that biological, psychological, and emotional factors can all impact how similar pain is perceived by different individuals.
Pain researchers believe regular exposure to painful stimuli can increase one’s pain tolerance. Some individuals learn to handle pain by becoming more conditioned to it. However, there is also evidence to support the theory that repeated exposure to pain can make a person respond more vigorously to minor pain in the future. (Source, emphasis mine)
While I'll certainly bow to a canonical reason, the Joker could (a) be born that way and (b) become desensitized through both emotional and physical exposure to pain. It helps that the character has been developed in a way that happens to be supported by these research findings.
Addendum: I'd like to point something out based on a comment from @CombatJacket. If we want to explain every one of the Joker's characteristics using Real Life knowledge, we could resort to Congenital Insensitivity to Pain and Anhydrosis (CIPA) Syndrome. The problem with doing this is that said syndrome comes with consequences, because pain serves a purpose and without it all kinds of problems come to pass — like infections that can kill you.
We live in a funny world right now. There's this odd quest to explain every fictional character, superpower, attribute, etc. using Real Life science — as if authors from 50+ years ago had inside knowledge about science or that the science we know today is the end-all of knowledge. Fortunately, neither is true (could you imagine how boring it would be if there was nothing left to learn?).
I'm actually hoping someone can bring some story canon to light to explain the Joker's tolerance to pain. It's much more interesting to see how a good author rationalized an otherwise unusual (if not downright impossible) characteristic. Keep in mind that half the time the rationalization came second and much later in the story — if it exists at all.
I guess my points are:
Real Life explanations for fictional characteristics are often unsatisfactory because they come with consequences that are almost never reflected in fiction. They're fun to play with, but they're not good fiction.
Substituting Real Life for a good imagination literally takes all the fun out of fiction. When investigating what could explain something, please don't lose sight of why you found it worth your time to try and explain in the first place: it was uber-cool and pulled you into the character's world. That's good fiction.