Can I download music from Apple Music onto a MP3 player?

If you got it through an Apple Music subscription, no.

If you actually bought it, drag the files to the player.

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If you are referring to the streaming version, no. You can download it for offline use but it requires Apple software (Music app) to play.

If it is music you purchased from Apple, you can, but it will be AAC format, not mp3. You would have to convert it to mp3 if your player really is mp3-only.

Redownload music - Apple Support