The structures appear to be 'lumps' in the thin gas that lies between the stars in our galaxy, researchers said.
"They could radically change ideas about this interstellar gas, which is the galaxy's star recycling depot, housing material from old stars that will be refashioned into new ones," said first author Keith Bannister, from the Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Australia.
The researchers described breakthrough observations of one of these 'lumps' that have allowed them to make the first estimate of its shape.
They figured out this behaviour was the work of our galaxy's invisible 'atmosphere', a thin gas of electrically charged particles which fills the space between the stars.
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"Lumps in this gas work like lenses, focusing and defocussing the radio waves, making them appear to strengthen and weaken over a period of days, weeks or months," Bannister said.
These episodes were so hard to find that researchers had given up looking for them.
Astronomers think the lenses are about the size of the Earth's orbit around the Sun and lie approximately 3,000 light-years away - 1,000 times further than the nearest star, Proxima Centauri.
Until now they knew nothing about their shape, however, the team has shown this lens could not be a solid lump or shaped like a bent sheet.
"We could be looking at a flat sheet, edge on. Or we might be looking down the barrel of a hollow cylinder like a noodle, or at a spherical shell like a hazelnut," said Cormac Reynolds, a CSIRO team member.
This means earlier optical surveys that looked for dark lumps in space could not have found the one his team has detected, Bannister said.
Researchers said that these lenses may be cold clouds of gas that stay pulled together by the force of their own gravity.
That model, worked through in detail, implies the clouds must make up a substantial fraction of the mass of our galaxy. Nobody knows how the invisible lenses could form.
The study was published in the journal Science.