Quick answer – No!
The phenomenon of pain is composed of two factors: physical sensation (painful symptoms) and how you feel about that sensation (discomfort).
In the context of a therapeutic massage, your physical sensation as a result of the work being done during a session should never be one of pain.
However, you may sometimes feel significant discomfort due to intensity of sensation. It is very important to report when that discomfort and intensity is too high in the context of a therapeutic massage. Having said that, a good massage therapist will usually know (and back off) when that is the case.
I would like to add that it is a misconception that therapeutic massage should be painful in order to be effective. I don’t believe in “no pain, no gain.”
It is important though that you have the experience that the work is doing something beneficial, and often intense sensation helps you to know that things are changing as a result of the massage and soft tissue manipulation going on.
Read more in my Frequently Asked Questions blog series:
Can I talk during a therapeutic massage?
How should I feel after a therapeutic massage?
What is chair massage?
Do I need to be naked during a therapeutic massage?
What to expect in a professional massage?
What is a Licensed Massage Therapist (LMT)?
What is a scope of practice? What is yours as an LMT?
What do you learn in massage school?
What kind of massage do you do?
What kind of music do you play during a massage?
Should I give you a tip after the massage?