This totally depends on what kind of massage you're thinking of. Most deep massages require a considerable amount of pressure - some masseuses will use their elbows or even heels. To achieve that - and, by the way, such a machine will be able to exert dangerous amounts of pressure - you're going to need hydraulics.
Soft or "finger" massages can use memory-form metals, pneumatics (here, for grips), or coil-and-wire setups (also called "spider motion" because this is how most arachnids' legs work; they're naturally bent, and the critter has to strain to distend them; the opposite of how human limbs work).
Then you have an additional form of massage which is not really feasible for humans: a tentacle can extert a considerable striction or compressive force, which may turn useful as a sort of lymphatic drainage massage on steroids.
However powered, your tentacles would probably end up being composed of a series of short, rigid sections with one, possibly two degrees of freedom each, one to "flex/bend" and one to (slightly) rotate. The last two or three sections on the tip could also be equipped with a piston (i.e. the tentacle tip can stretch forward), adding a third degree of freedom.
One thing the massaging tentacles would surely need is a biocompatible, sturdy silicon skin. Optionally they might need heating for comfort, and for special purposes the capability of delivering electrical currents. Support for vibration could also be a plus.
The tentacles would require some way of analyzing the part being massaged (if only to be sure they're not accidentally kneading your carotid sinus). The best way would probably be via ultrasound (as @AndyD273 observed, this would recommend coating the imaging tentacles with ultrasound gel, i.e. slime. That might be a plus or a minus depending on the scenario).
For approaching the part, some kind of camera would be needed. The capability of such a camera to "see" into the infrared could also turn out to be useful as it would allow to estimate blood flow.
In case someone wanted to implement specially purposed tentacles (the scientific term would be hectocotyli) little would need to be done except modifying the controlling software; there could even be a black market of creative mods.