Can I play Pokémon Sun and Moon purchased in another country?

From the Nintendo Support Forums, this same question was asked and this answer was chosen by the moderator as the best answer:

No. Nintendo 3DS games and systems are both region-locked, so a German copy of Pokémon Sun would only work on a Nintendo 3DS system from that same region. Similarly, a NTSC Nintendo 3DS system would only be able to play a Pokémon Sun game from the NTSC region.

Therefore, Pokemon Sun and Moon are region-locked and you will not be able to play a Chinese or Taiwanese copy on your Japanese 3DS.

For a map of the regions that Nintendo locks according to, see here.

According to the region locking wikipedia page the 3DS is region locked for 3DS specific software. So I think you may be out of luck until you get a Japanese copy of the game.

Source: https://en.wikipedia.org/wiki/Regional_lockout#Nintendo

The Game Boy and Nintendo DS product lines do not use regional lockouts for physically distributed games; however, software specific to the Nintendo DSi are region-locked, and cartridges released by iQue in China can only be played on DS models produced by iQue (although they remain compatible with other DS cartridges). The Nintendo 3DS line however, does enforce region locking for 3DS-specific software,[2] with the exception of Nintendo 3DS Guide: Louvre, which is region-free.