"The Monster from Nowhere", a short story by Nelson S. Bond, also the answer to this old question; originally published in Fantastic Adventures, July 1939, available at the Internet Archive. It starts on p. 291 of the 1963 paperback edition of Groff Conklin's 1946 anthology The Best of Science Fiction.
The thing changed! As I watched, there seemed to be, at one time, a globular piece of matter twisting on the rod. An instant later, the globe had turned into a triangle—then into something remotely resembling a cube. It was constantly in motion; constantly in flux. But here is the curious part. It did not change shape slowly, as an amoeba, so that you could watch the sphere turn into an oblong; the oblong writhed into a formless blob of flesh. It made these changes instantaneously!
The "Flatlander" in the following excerpt is not a real character in the story, he's part of a thought experiment used to explain the concept.
I said, "I told you I didn't have a scientific mind, Butch. What does all this mean?"
Butch said patiently, "I have merely been establishing a thought-pattern, Len, so you can grasp the next step of my reasoning. Forget the Flatlander now—or, rather, try to think of us as being in his place!
"Would we not, to a creature whose natural habitat is a higher plane than ours, appear much the same sort of projection as the Flatlander is to us?
"Suppose a creature of this higher plane projected a portion of himself into our dimension—as I projected my finger into Flatland. We would not be able to see all of him, just as the Flatlander could not see all of us. We would see only a tri-dimensional cross-section of him; as the Flatlander saw a bi-dimensional cross-section of us!"
This time I got it. I gasped:
"Then you think that thing in the work-shed is a cross-section of a creature from the—"
"Yes, Len. From the Fourth Dimension!"