The D&D themed Star Wars fan webcomic Darths & Droids has recently published a footnote about magic flasks and what happens to the flasks that contain the potions:
Imagine a magic potion flask. If the PCs detect magic, of course it gives off an aura of magical power, but then they expect that from the potion inside anyway. Nobody suspects the flask itself.
By the way, what do PCs do with the flasks when they drink a magical potion? Has anyone ever asked this question before? The players usually just cross/erase used potions off their equipment lists. Where do the flasks go? Are all dungeons littered with the empty potion flasks of previous adventuring groups, like discarded cans and bottles by the side of the road?
Anyway, make a point of having the PCs find all their empties when they make camp and take stock of their gear. What are they going to do with these empty flasks? If they're like most adventurers, they might try to sell them, or perhaps they'll fill them with holy water or something. Here's where you have the magic of the flask step in. Maybe it always returns to their pack, no matter how they try to get rid of it. Maybe it converts whatever it contains into the same potion that was originally found in it (once per week, say, so it's not overpowered). Maybe it does something else completely, like attract monsters, or prevent any fires from being lit within 30 feet.
Who would suspect a flask?
Emphasis mine, and it's exactly that which I'd like to ask about: Is there a rule or a dev comment about what happens to the flask of a magical potion?
Since Darths & Droids doesn't specify a system (or rather says they use a homebrew system), assume D&D 5e as the version, since that's the most recent one. However, if D&D 5e does not contain information about this, earlier versions of the game are also acceptable.
Best Answer
The flask is saved for when the DM asks you "do you have any glass containers" when you are trying to harvest a blood, poison or venom from vanquished monster.
People then try frantically to calculate how many health potions they have drank recently to convince the DM they have a lot of glassware that can be used to contain the valuable ingredients.
RAW there is no info on that - the bottle does not magically vanish. You end up with an "empty health potion flask" you can do as you wish. If you don't really note it down it can be assumed you just threw it away. If you do - you have put it in your backpack.