Until two years ago, quasicrystals had only been created in the lab - then geologists found them in rocks from Russia's Koryak mountains.
In PNAS journal, a team says the chemistry of the Russian crystals suggests they arrived in meteorites.
Quasicrystals were first described in the 1980s by Israeli researcher Daniel Schechtman, who was awarded last year's Nobel Prize in Chemistry for the discovery.
Schechtman's ideas were initially treated with doubt or scorn by some of his peers, who thought the structures were "impossible".
Rule breaker Quasicrystals break some of the rules of symmetry that apply to conventional crystalline structures. They also exhibit different physical and electrical properties.
In 2009, Luca Bindi, from the University of Florence, Italy, and his colleagues reported finding quasicrystals in mineral samples from the Koryak mountains in Russia's far east.
The mineral - an alloy of aluminium, copper, and iron - showed that quasicrystals could form and remain stable under natural conditions. But the natural process that created the structures remained an open question.
Now, Dr Bindi, Paul Steinhardt from Princeton University and others claim that tests point to an extra-terrestrial origin for the Russian minerals.
They used the technique of mass spectrometry to measure different forms - or isotopes - of the element oxygen contained in parts of the rock sample.
The pattern of oxygen isotopes was unlike any known minerals that originated on Earth. It was instead closer to that sometimes found in a type of meteorite known as a carbonaceous chondrite.
The samples also contained a type of silica which only forms at very high pressures. This suggests it either formed in the Earth's mantle, or was formed in a high-velocity impact, such as that which occurs when a meteorite hits the Earth's surface.
"Our evidence indicates that quasicrystals can form naturally under astrophysical conditions and remain stable over cosmic timescales," the team writes in PNAS