The Mars Helicopter will be bundled with the US space agency's Mars rover when it launches in 2020.
Its design team spent more than four years shrinking a working helicopter to "the size of a softball" and cutting its weight to 1.8kg (4lbs).
Nasa provided this computer-generated image of the helicopter's design
It is specifically designed to fly in the atmosphere of Mars, which is 100 times thinner than Earth's.
Nasa describes the helicopter as a "heavier-than-air" aircraft because the other type - sometimes called an aerostat - are balloons and blimps.
Soviet scientists dropped two balloons into the atmosphere of Venus in the 1980s. No aircraft has ever taken off from the surface of another planet.
The helicopter's two blades will spin at close to 3,000 revolutions a minute, which Nasa says is about 10 times faster than a standard helicopter on Earth.
"The idea of a helicopter flying the skies of another planet is thrilling," said Nasa Administrator Jim Bridenstine.
"The Mars Helicopter holds much promise for our future science, discovery, and exploration missions to Mars."
While the tiny craft is being called a helicopter rather than a drone, there will be no pilot.
t will be flying almost 55 million km (34 million miles) from Earth, too far away to send a remote control signal.
"Earth will be several light minutes away, so there is no way to joystick this mission in real time," said Mimi Aung, the project manager at Nasa's Jet Propulsion Laboratory.
Instead, the helicopter will "fly the mission on its own".