You can bring your herbal medicine to Japan, but without any application if the quantity is up to 1 month worth.
If you want to bring more than that amount, you have to apply for Import Confirmation (...Yunyu Kakunin-Sho).
Through the link here, you can find more information and format of document you need to submit.
https://kouseikyoku.mhlw.go.jp/kantoshinetsu/iji/yakkanhp-kaishu-2016-3.html
* Japanese only
Please fill out the forms and submit them to Kanto-Shinetsu Regional Bureau of Health and Welfare via Email(yakkan@mhlw.go.jp).
They will check the forms and if there`s no problem or objections, they will send you Yunyu Kakunin-Sho.
They say it will take approximately 7days to issue the Yunyu Kakunin-Sho.
So please make sure to submit the forms with well in advance.
Reference: https://kouseikyoku.mhlw.go.jp/kantoshinetsu/iji/bana-warifuri.html
You can bring your medication in the luggage bag.