Xbox 360 and PC versions are available to download now from torrent websites, according to CVG.
It has also been sold early by retailers across Europe, leading to a number of usermade videos appearing online.
Design director David Vonderhaar commented on the early leaks, saying that posting live streams of footage is something "I don't remotely recommend" but joked that players should "at least be good at it".
"I'm really glad people are excited for the game. Legit streams coming up later this week and early next. Watch this space," he said.
Halo 4, which launches worldwide tomorrow (November 6), has experienced similar early leaks
Earlier this month, Activision confirmed that Call of Duty Elite will drop its annual subscription, and will instead opt for a Season Pass for Black Ops 2.
Black Ops 2 will be available on Xbox 360, PS3 and PC from November 13 worldwide, and on Wii U from November 30 in Europe.
> 'Black Ops 2' multiplayer preview: Six anticipated new features
Screenshot gallery - images of Black Ops 2 below: