Little Music Player is the smallest I could find, clocking in at a whopping 21.7 KB but it might be a bit barebones even for your taste.

A deeper search uncovered Kure Music Player which has a bit more features but hasn't been updated since 2014. How vital is it that the app be under 1 MB?

The smallest music player app I've seen is Apollo Music Player, but it's 2.16 mb

May I ask why the requirement of under 1mb? Do we speak about RAM usage or install size (or download size)?

Little music player is about 20kb

I use SicMu Player, it's 2.5 mb.

It's 10Mb, but here's Fossify's Music Player: Fossify Music Player on FDroid

Tiny Music Player is only 16KB!