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.
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 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.