It’s not grammatically wrong (“a Japanese” is the one and only demonym for a person from Japan), but the trend in recent decades is to avoid using nationality words ending in “-ese” as nouns. It just sounds a little awkward nowadays, and some overly sensitive people may eveb think it sounds somehow “racist” or something like that. I’d recommend that you just use the adjective.

Hi Yusuke, I’d expand on Phil’s good answer by saying that English is weird about demonym (people-naming, like nationality word) suffixes that aren’t -ian or -an. -ese and -ish and -ch all make nouns that sound off, although they’re fine as adjectives: “I’m a Japanese” sounds wrong in the same way “I’m a French” or even, ironically, “I’m an English” does. (This is how I’d answer any objections on the grounds of racism: it’s just what suffix the language assigns you, not something about your ethnicity.) But the solution in all these cases is to add “man” or “person” to the demonym, and make it an adjective: Englishman/woman, Frenchman/woman. “I’m a Japanese man/woman/person”.