The Japanese notary public generally notarizes documents other than public documents (private documents such as wills, contract/agreement, power of attorney/letter of appointment or translation of public documents), but they can notarize a passport (which is a public document) as an exception. This is called a passport authentication (“passport ninsho” in Japanese). Legal specialists such as Immigration Lawyer/Attorney at Administrative Procedures (Gyoseishoshi) or Attorney at Law (Bengoshi) can do passport certification and this is called “Passport Shomei” in Japanese.
It is recommended that you check with the institution to which you are required for passport notarization/authentication/certification whether they accept a document certified by a legal specialist other than notary public in Japan as they are accepted by many financial institutions outside of Japan (for keeping accounts, residence/address certification, to be attached with Power of Attorney, etc.)
FYI, passport authentication by a notary public costs JPY11,500 per document (documents written in English) and the service fee by legal professional vary in the range between JPY5,500 and 33,000.
If you are a US citizen, or the document in question is for the use in the US, you may have it notarized by a US Consulate in the US Embassy/Consulate in Japan. Their service fee is USD50 per document, and you need to make an appointment through their website.
https://jp.usembassy.gov/u-s-citizen-services/notarial-services/

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