The bug is tied to a Templar follower encountered early in the game. Attempting to trade an item that is already equipped on your character to the Templar results in the game disconnecting from Battle.net servers.
Users who try to log back in after being disconnected receive an error 3006 message, preventing them from logging back into the game.
Blizzard has stated that it is aware of the bug, and is currently working on a hotfix to resolve the issue.
Diablo 3 has had a rocky first day, with many users unable to log in due to an overcapacity on servers. In response, Blizzard temporarily took down its own Battle.net website to free up more servers for Diablo 3.
Digital Spy experienced similar connection problems during last night's live first impressions.
To mark the release of the long-awaited sequel, Blizzard has announced that it will hold a series of global events to celebrate its launch.
A Collector's Edition of the game will be available at retail, which includes the game's soundtrack, a two-disc behind-the-scenes DVD and Blu-ray set, an art book and a 4GB USB soulstone flash drive loaded with the full games of Diablo 2 and its expansion Lord of Destruction.
Blizzard is also offering Diablo 3 free to users who sign up for the World of Warcraft annual pass, a yearly subscription to the popular MMO.
A Starter Edition of the game has also been confirmed, offering a limited introduction to Diablo 3 with content similar to its private beta.
Watch the Diablo 3 launch trailer below: