Can a therapeutic massage cause harm to a herniated disc?

Very unlikely. The amount of force applied to the spine during massage is relatively minimal unless some kind of manipulation is done at the same time. For this reason, it is very unlikely that a massage could cause further harm with a disc herniation.
No. Aa long as you are not ignoring any significant symptoms like bowel or bladder control issues or a progressive weakness in an extremity, most disc herniations are treated nonoperatively-90%.