Does Sona's passive work on inhibitors?

This has been confirmed by Riot to be a bug, and it will be fixed in an upcoming patch.

Source:

just tested a fix for this—going to try to get it into the next release. looks like powerchord was set up to deal damage to inhibitors and the nexus (which is why it was consumed) but a bug was preventing it from being applied. we're just going to fix the bug, so sona will be able to powerchord inhibitors (and the nexus) when that goes out.

you can't diminuendo or slow structures though, so be mindful of that if you're going to use your passive for extra damage.

No, it does not.

Sona's passive deals damage to turrets, champions, minions, and creeps.
Sona's passive does not deal damage to (or get consumed by attacking) inhibitors or the nexus.

From leagueoflegends.wikia.com:

Power Chord will not trigger if attacking an enemy inhibitor or nexus, but the animation and sound will still play (over and over again, because the Power Chord is never actually spent).

Abilities that damage turrets