At the risk of being a bit unoriginal, I would emphasize the Japanese aspect (just the way Swiss pharmaceutics laboratories emphasize being Swiss).
So, perhaps a hint of brush would work, for example.

1) Be subtle.
2) Worry about how your font's aesthetics will translate online/onscreen.

hhp

Azuki has a kind of Asian brush feel without mocking Chinese(–Japanese) ductus.
http://www.myfonts.com/fonts/bluevinyl/azuki/

Caturrita is interesting, though seems to have some spacing bugs.
http://www.myfonts.com/fonts/armasen/caturrita/
http://www.myfonts.com/fonts/armasen/caturrita-extra/
http://www.myfonts.com/fonts/armasen/caturrita-display/

Eidetic: http://www.myfonts.com/fonts/psyops/eidetic-modern/
There is also a Serif to that.

I also find Bluegrass worth a try:
http://www.myfonts.com/fonts/scrowleyfonts/bluegrass/

And surely Fertigo and Ferigo Script might be interesting as well...
http://www.myfonts.com/search/Fertigo/fonts/

Oh come on, is the cliché for Japanese still good olde gesticulative brushwork?
This has been one of the leading high-tech countries for the past 50 years.
One of my best friends as a teenager (we spent a lot of time under the covers with the lights out):

Sony US branding from the 1960s leveraged its Clarendon wordmark:

Admittedly, high tech is not herbal, but nonetheless, Clarendon doesn’t exactly spring to mind for high tech, does it?

But if you really want to go all brushy, it would be hard to top Papyrus!

But do people really know/feel that Sony is Japanese?

hhp

Clichés are important, for marketing reasons.

Nick, this is for Japanese herbal medicine, not Japanese consumer electronics.

I think people understand that Japan, and Japanese visual culture, has both (very) modern/futuristic and (very) ancient/mysterious/foreign (from a Western perspective) sides. «Japanese» isn't enough to decide on a design direction; «Japanese high-tech» or «Japanese traditional», at least to me, point in vastly different directions.

One of my favorite kinda-Asian-calligraphy-vibe faces...

http://www.fonts.com/findfonts/detail.htm?productid=47382

Maybe Akira Kobayashi's ITC Woodland? Though I don't know how suited it is to web use.

Thanks so much for lots of suggestions!

Japanese herbal medicine 'Kampo' actually has both traditional way of understanding the body and scientific analysis of the effectiveness.
So that, I think I would choose these typefaces having gentle blush/calligraphic serifs but still looking contemporary.

http://www.myfonts.com/fonts/linotype/itc-woodland/
http://www.myfonts.com/fonts/psyops/eidetic-modern/
http://www.myfonts.com/fonts/armasen/caturrita/