I used to practice karate earlier. 5 years ago I was diagnosed with minor disc herniation at L4 and L5. I haven't undergone any surgery and pretty much cured just by physiotherapy and can do all my day to day activities without any problem. I do a little bit of yoga everyday as suggested by the doctor. I want to restart my martial arts training. Is it safe to do so?
Tony's answer is great, I won't repeat it here, though it's largely what I would have written.
I will add that I had a herniated disk when I was in my early 20's while in, and certainly exacerbated by, my martial arts practice (I think also L4/L5). With extensive physiotherapy, I avoided surgery, and did (several months later) ease gradually back into martial arts practice. That was 20 years ago, during which time I have studied various martial arts on and off. I'm careful to have good posture, good sitting and exercise habits, avoid things that would be especially straining on my lower back, and generally try to keep my core strength up to support the region. Being vigilant about those things, once I recovered fully, I have not found it to be an impediment to my martial arts training. So -- all caveats in place with a sample size of one -- it certainly can be done.
Go over it with your own doctor, don't do anything that hurts, but if you are already recovered enough that you don't notice it in your daily life and you're doing other exercise without incident, I don't see why you shouldn't try martial arts again.
Disclaimer: I have no medical background. Please consult your Doctor.
First and foremost, (and I really can't say this enthusiastically enough) Please consult your Doctor! His/her word will be much more valuable than anything you read here. Second, I suspect that it should probably be OK to start up again, but do so very cautiously. Here are some (non-medical, common sense) things to keep in mind: