The subterranean ocean is thought to have more water than all the water on Earth's surface, researchers said.
Identifying liquid water is crucial in the search for habitable worlds beyond Earth and for the search for life.
"This discovery marks a significant milestone, highlighting what only Hubble can accomplish," said John Grunsfeld, assistant administrator of NASA's Science Mission Directorate at NASA Headquarters, Washington, DC.
"A deep ocean under the icy crust of Ganymede opens up further exciting possibilities for life beyond Earth," said Grunsfeld.
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Because Ganymede is close to Jupiter, it is also embedded in Jupiter's magnetic field. When Jupiter's magnetic field changes, the aurorae on Ganymede also change, "rocking" back and forth.
By watching the rocking motion of the two aurorae, scientists were able to determine that a large amount of saltwater exists beneath Ganymede's crust, affecting its magnetic field.
A team of scientists led by Joachim Saur of the University of Cologne in Germany came up with the idea of using Hubble to learn more about the inside of the moon.
If a saltwater ocean were present, Jupiter's magnetic field would create a secondary magnetic field in the ocean that would counter Jupiter's field.
This "magnetic friction" would suppress the rocking of the aurorae. This ocean fights Jupiter's magnetic field so strongly that it reduces the rocking of the aurorae to 2 degrees, instead of 6 degrees if the ocean were not present.
Scientists first suspected an ocean in Ganymede in the 1970s, based on models of the large moon. NASA's Galileo mission measured Ganymede's magnetic field in 2002, providing the first evidence supporting those suspicions.
The new observations were done in ultraviolet light and could only be accomplished with a space telescope high above Earth's atmosphere, which blocks most ultraviolet light.
The finding was published in the Journal of Geophysical Research: Space Physics.