Diablo – How to access the Auction House from out of game

Unfortunately the Auction Houses are only accessible from the menus, not anywhere in the game via your character.

The Auction House is a new trading system introduced in Diablo III which shares many features with similar systems found in other games, such as World of Warcraft. Accessed through Battle.net and not from in-game, the auction house allows all players within a region (US, EU etc.) to buy and sell items easily and conveniently between each other. Almost all items other than quest items can be sold between players, and everything is run by the players: Blizzard will not sell any items.

http://www.diablowiki.com/Auction_House

Edit: Blizzard has since confirmed that this is a deliberate design decision (Source).

Contrary to MMOs like World of Warcraft Diablo III is not a game where the auction house meta-game is part of the in-game story.

For anyone coming across this, the auction house (both gold and real money one) was removed from the game in 2014. https://us.battle.net/forums/en/d3/topic/9972208129