The hollow ball with a circumference of 1.1 metres (43 inches) was found near a village in the north of the country some 750 kilometres (480 miles) from the capital Windhoek, according to police forensics director Paul Ludik.
Locals had heard several small explosions a few days beforehand, he said.
With a diameter of 35 centimetres (14 inches), the ball has a rough surface and appears to consist of “two halves welded together”.
It was made of a “metal alloy known to man” and weighed six kilogrammes (13 pounds), said Ludik.
It was found 18 metres from its landing spot, a hole 33 centimetres deep and 3.8 meters wide.
Several such balls have dropped in southern Africa, Australia and Latin America in the past twenty years, authorities found in an Internet search.
The sphere was discovered mid-November, but authorities first did tests before announcing the find.
Police deputy inspector general Vilho Hifindaka concluded the sphere did not pose any danger.
“It is not an explosive device, but rather hollow, but we had to investigate all this first,” he said.