Seth Bling, from Seattle, described his project online in a video.
The ones and zeroes used by computers as the basis for all programming are represented by alternating blocks - either dirt or stone.
However, the emulator is too slow to actually be playable - a single game could take months.
Mr Bling's console comprises a giant screen, which gradually updates as the game animates, and a huge field of blocks that form the virtual console's memory.
He has also designed game cartridges for Donkey Kong, Space Invaders and Pac Man - in the form of huge Minecraft blocks that are scanned as though being read by the original hardware.
Two thousand command blocks - which can perform operations on other blocks - form the system's processor. They manipulate blocks in the memory just like a physical processor operates on data in a computer.
But the processor works very slowly, drawing frames to the screen 60 times every four hours. The original console ran at 60 frames per second.
"Because of the structures that exist within Minecraft [...] you could, weirdly, in an Inception-like way, build a Minecraft within Minecraft," said Tom Crick, professor of computer science and public policy at Cardiff Metropolitan University, referring to the film.
The possibilities, he added, were more or less boundless.
"You could very easily construct a modern Intel or ARM microprocessor - it would be very slow but it would be functionally correct and complete," he told the BBC.
He pointed out that, in the physical world, Lego also allows people to build all kinds of mechanical devices on a large scale.
The game's developer, Mojang, released an educational edition of the game earlier this year and parent company Microsoft recently unveiled a one-hour online tutorial, built entirely in Minecraft, that teaches students to code.
But last month, the UK government's "behaviour czar" Tom Bennett told The Times newspaper he was "not a fan" of Minecraft in lessons.
"This smacks to me of another gimmick which will get in the way of children actually learning," he said.
Prof Crick said Minecraft was not a magical tool that solves educational problems, but added, "The fact you can create essentially anything is a very powerful thing."
A YouTuber has recreated the Atari 2600 games console - by building a virtual version of the device's hardware out of Minecraft blocks.