According to ergoproxy.wikia.com (note that the second paragraph contains spoilers for anyone who hasn't watched the whole series):
The series takes place in a post-apocalyptic future of Earth, focusing on the aftermath of a global ecological disaster. The apparent cause of this travesty was rapid climate change due to a string of explosions in methane hydrate reserves. Occuring during the second half of the 21st century, the impromptu detonations succeeded in wiping out 85% of the planet's Human population.
In order to survive, the remaining Humans made 300 Proxies in an event known as the Proxy Project and charged them with the creation of another Human race; they were to be nurtured within Dome Cities of the Proxies' establishment. These sealed off communities contained a birthing system called the WombSys as well as AutoReivs, two factors intended to aid and propagate the fledgling species. Once the Proxies were sent forth, the original Humans left Earth for another planet, biding their time until they were certain that Earth was safe for both Human races to settle. Their purpose completed, the then obsolete Proxies would have their immortal Amrita Cells destroyed by the emerging sun's deadly rays, unable to live under blue skies and therefore stamped out as relics of the past.
So to summarize, it does take place on earth/in our world following a post-apocalyptic event.