They will ship to Japan with no problem whatsoever.
The only issue you have is that many items they stock cannot be shipped outside of the USA.
If you are shopping from Japan then you should start at the AmazonGlobal page which only shows you all items on Amazon that can be shipped overseas.
Is Amazon available in Japan?
Amazon Japan international shipping options. Amazon Japan can ship some of its items to more than sixty countries in the world. Unfortunately, all sellers are not using that feature. We’ve created a proxy-buying service that allows you to buy on Amazon Japan.
Can you use US Amazon account in Japan?
Yes, you can easily order from Amazon Japan. In fact, not only do they ship to US but over 65 other countries. Same item from Amazon Japan can be purchased for 8,489 YEN, which is equivalent to $69. Shipping is around $13 via DHL Express to USA.
Does Amazon Japan ship internationally?
Customers will need to look for items sold directly by Amazon.co.jp — not third-party sellers — and those that qualify for shipping through AmazonGlobal International Shipping. So shop carefully with the knowledge that not everything you might want to import via Amazon Japan will be available to ship internationally.
Does Amazon Prime ship free to Japan?
Any item with “FREE Shipping” messaging on the product detail page that is fulfilled and shipped by Amazon is eligible and contributes to your free shipping order minimum. You can get unlimited FREE Two-Day Shipping on eligible items with Amazon Prime. No minimum spend is required to qualify.