A phenomenon this large has never before been seen around any exoplanet, researchers said.
The cloud of hydrogen has been dubbed as "The Behemoth" bleeding. The hydrogen is evaporating from the planet because of the extreme radiation from the star.
Given this planet's small size, it may offer clues to how hot super-Earths - massive, rocky, hot versions of Earth - are born around other stars through the evaporation of their outer layers of hydrogen.
"This cloud is very spectacular, though the evaporation rate does not threaten the planet right now," said the study's leader, David Ehrenreich from the Observatory of the University of Geneva in Switzerland.
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The planet, named Gliese 436 b (GJ 436b), is considered to be a "warm Neptune," because of its size and it is much closer to its star than Neptune is to our Sun.
Although it is in no danger of having its atmosphere completely evaporated and being stripped down to a rocky core, this planet could explain the existence of so-called hot super-Earths that are very close to their stars.
Because the planet's orbit is tilted nearly edge-on to our view from Earth, the planet can be seen passing in front of its star. Astronomers also saw the star eclipsed by "The Behemoth" hydrogen cloud around the planet.
Ehrenreich and his team think that such a huge cloud of gas can exist around this planet because the cloud is not rapidly heated and swept away by the radiation pressure from the relatively cool red dwarf star.
This allows the cloud to stick around for a longer time.
If so, Earth may previously have sported a comet-like tail. It's also possible it could happen to Earth's atmosphere at the end of our planet's life, researchers said.
GJ 436b resides very close to its star - less than 3 million miles - and whips around it in just 2.6 Earth days.
This exoplanet is at least 6 billion years old, and may even be twice that age. It has a mass of around 23 Earths. At just 30 light-years from Earth, it's one of the closest known extrasolar planets.