It's never quite explained in-game where the Mani Mani statue comes from. It is 'found' underground, appears to have an evil power eminating from it, and also seems to be able to go to and from places of its own accord, spreading evil wherever it goes...but where did it come from, and how did it get to Earth?
There's some fan theories about it's purpose/creation but nothing is ever explicitly said about it's origins, and there aren't many hints regarding it that I ever noticed either. It was dug up under Liar X Aggerate's house and caused several relevant events over the course of Earthbound (Mother 2) but no origins are really stated.
There might be minor Mother 1 or Mother 3 spoilers in the following paragraphs and presumably the reader has finished Mother 2. Too much to spoilerize it all.
Interestingly there's never even a very direct link to Giygas (Though Monotoli, after being under the influence of the Mani Mani statue admits the statue told him to stop Ness, then mutters "the name evil Giygas...or something like that "), though the two seem to further the same goal (Evil) and are described as being, more or less, evil incarnate, and both seem to be able to contort people's minds to make them crazy/dangerous.
Despite the obvious similarity there's really nothing that I can recall that directly links the two so clearly as "Giygas made the Mani Mani Statue" or "Giygas is controlling/manipulating the Mani Mani Statue" though the events in the game make it extremely unlikely that both Giygas and Mani Mani "activated" at around the same time by coincidence.
In case you haven't played them, there's no Mani Mani statue or direct (or, that I could at any point glean, implied) connection to the Mani Mani statue in Mother 1 or Mother 3 of any kind. It doesn't even show up in the piles of Mother 2 references in Mother 3.
The location of the Mani Mani statue deep underground seems to make it unlikely that it's existence is the result of anything that occurred in Mother 1 (the game took place only ~10 years earlier); the location/appearance of the Mani Mani statue appear to suggest some sort of ancient evil. Gyiyg's plotline in the first game starts 100 years before Mother 2 which doesn't quite fit "ancient evil" but I suppose it's possible it had something to do with Gyiyg's race and their PSI powers, as they visited earth at that time in 1909.
So it while seems very clear that Giygas and Mani Mani had some connection, nothing is really stated or even implied. Gyiyg/Giygas is the focal point of Mother 1, but it doesn't appear in that game at all, so it doesn't seem inexorably tied to Giygas. And it doesn't appear at all in Mother 3 so it doesn't seem to be any over-arching evil. I would say it's true purpose is either deliberately left ambiguous or it's simply another one of Giygas' minions/effects on the world; honestly the specific origins of much weirdness in Mother 2 go unexplained and a quiet assumption of "Giygas did it" is usually best.