http://paizo.com/prd/magicItems/magicItemCreation.html
create magic items, spellcasters use special feats which allow them to
invest time and money in an item's creation. At the end of this
process, the spellcaster must make a single skill check (usually
Spellcraft, but sometimes another skill) to finish the item. If an
item type has multiple possible skills, you choose which skill to make
the check with. The DC to create a magic item is 5 + the caster level
for the item. Failing this check means that the item does not function
and the materials and time are wasted. Failing this check by 5 or more
results in a cursed item (see Cursed Items for more information).
Note that all items have prerequisites in their descriptions. These
prerequisites must be met for the item to be created. Most of the
time, they take the form of spells that must be known by the item's
creator (although access through another magic item or spellcaster is
allowed). The DC to create a magic item increases by +5 for each
prerequisite the caster does not meet. The only exception to this is
the requisite item creation feat, which is mandatory. In addition,
you cannot create potions, spell-trigger, or spell-completion magic
items without meeting their spell prerequisites.
You can use spellcraft or craft(alchemy) for the final check to create the potion/oil, but the brew potion feat is still required.
Ok. This is a bit of a tricky one. Potions of Healing, while created of magical substance aren't actually considered magic items. Or are they.
They aren't magic items
Note, for instance, that they aren't listed as "magic items" in the DM book we've seen so far (BD&D DM Book pp 59-60, v.1). They are listed in the "Adventuring Gear" section of the Players book in basic (BD&D Players Book pp. 48-50 v.2).
In other words, potions of healing aren't magic items in the sense that we think of magic items. They're much, much more common and easily brewed. So following the crafting rules in the PHB should be just fine.
They are magic items
Note for instance they are listed as magic items in the Starter Set DM book (LMOP 53). The entry does say that they are a magical red fluid.
Also of note is the Adventurer's League instructions call them out as a specific magic item that can be purchased by adventurers, not subject to the normal lack of magic item economy in organized play games.
So where does this leave us? In a great deal of confusion on this issue until December. Largely this is because the crafting rules beyond the mundane have been left to DM discretion (with the possibility of further guidance in the DMG). So the answer to this question is, ultimately, if you're a player, discuss it with your DM. If you're a DM, talk to your players and make a ruling. Considering the free and easy access to healing potions, I think it makes sense to allow their crafting, but if you wanted to limit them, that would be a reason to make them hard to craft. Judge the tone of your campaign.
DMG Update
Potion brewing is covered under crafting magic items in the DMG. Under these rules, the potion's rarity determines the potency, but also the amount of time and money it requires to brew. Under these rules, a common healing potion (which normally can be bought for 50 gp), requires 4 days and 100 gp to craft (and cannot be crafted until 3rd level and even then only by a character with spell slots). This is probably not a sensible way to obtain healing potions without a house rule.
Xanathar's Update
Xanathar's Guide provides optional rules for crafting during downtime. In particular, the optional rules (XGE, p 130) under "Crafting an Item" state:
Potions of healing fall into a special category for item crafting, separate from other magic items. A character who has proficiency with the herbalism kit can create these potions. The times and costs for doing so are summarized on the Potion of Healing Creation table.
Type |
Time |
Cost |
Healing |
1 day |
25 gp |
Greater healing |
1 workweek |
100 gp |
Superior healing |
3 workweeks |
1,000 gp |
Supreme healing |
4 workweeks |
10,000 gp |
Best Answer
The Dungeon Master's Guide lists "Crafting a Magic Item" as an option under "More Downtime Activities" (p. 128–129):
The DMG then provides an example, and suggests that the DM may also require that certain items need special materials or locations in order to be made, such as alchemist's supplies to brew a certain potion.
The DMG continues:
(The halved cost for consumables is a correction stated in the DMG errata.)
The Crafting Magic Items table is as follows:
The potion of invisibility magic item has a rarity of "very rare", so the creation cost would be 25,000 gp (halved from 50,000 because it's a consumable) and the minimum level needed to craft it would be level 11.
Technically, the description of the potion of invisibility doesn't say it creates the effect of the invisibility spell, so any character of the relevant level could presumably craft one. (However, a DM could house-rule that it creates basically the same effect as the invisibility spell and has the same duration (without requiring concentration), and thus that it would also need to be crafted by someone who has a 3rd-level spell slot and knows the invisibility spell.)
Given that creation cost, it would take a single character of the requisite level 1,000 days to craft one potion of invisibility, spending 25,000 gp to do so.
Note that the DMG does include rules on assisting in making a magic item:
So, for instance, if the character is in a party with 3 others of 11th level or higher, they can help contribute to the cost in terms of time and money (and spell slots and components if relevant). With a wizard crafting the potion and 3 other characters assisting, the total creation cost (25,000 gp) would remain unchanged but the process would only take one-fourth as long: 250 days.