If he is an adult then please don't tell his workplace. You'll lose his trust completely and he could be penalized for it, despite it being something that is likely out of control. Talk to him about it, but don't try to force him into anything. Let him know that you're there for him, that when he feels like he needs to hurt himself he can talk to you instead. He won't always, self-harm isn't something that goes away over night, but if he feels that support is there then maybe it will help him stay more level headed some of the time.
Acknowledge that self-harm releases chemicals that are a sort of 'salve' to negative emotions, and raise the topic of medication. Many people are put off by the idea of therapy, it can be hard to talk about issues. If he accepts that self harm feels like it helps in the moment due to a neurological 'release' of sorts, then he may be open to medication as an alternative. Once he's on medication, things may start to clear up a bit for him and he might decide to pursue therapy such as CBT or simple talk therapy. Just keep in mind that medication isn't a cure, but that it can make helping oneself a lot easier and so lead to recovery that way.
You haven't detailed the type of self harm, but if you're nearby when he does it then help him clean any injuries after the fact. Keep an eye on them in case medical treatment is needed. Try your best not to be judgmental/disappointed/angry etc... It's hard, you're only human, so don't beat yourself up if in the moment you react in a way you later regret.
If, after you talk to him about the above, he is still refusing help then try to decide which family member is best to step in and help. People, especially older people, may have certain, negative views or biases surrounding mental illness. Try to pick someone that loves him and is generally supportive. Let him know that you feel like you have to tell someone as you don't want to see him hurting anymore. Don't spring an intervention on him.
With all that said, make sure you have someone to talk to if you feel you need it. Sometimes loving and caring for someone with mental illness can be emotionally taxing.