Researchers said that though it is impossible to confirm the exomoon's presence, the finding is a tantalising first step toward locating others.
The discovery was made by watching a chance encounter of objects in our galaxy, which can be witnessed only once, researchers said.
"We won't have a chance to observe the exomoon candidate again," said David Bennett of the University of Notre Dame, and lead author of a new paper on the findings appearing in the Astrophysical Journal.
The international study is led by the joint Japan-New Zealand-American Microlensing Observations in Astrophysics (MOA) and the Probing Lensing Anomalies NETwork (PLANET) programmes, using telescopes in New Zealand and Tasmania.
Their technique, called gravitational microlensing, takes advantage of chance alignments between stars.
When a foreground star passes between us and a more distant star, the closer star can act like a magnifying glass to focus and brighten the light of the more distant one. These brightening events usually last about a month.
If the foreground star - or what astronomers refer to as the lens - has a planet circling around it, the planet will act as a second lens to brighten or dim the light even more.
By carefully scrutinising these brightening events, astronomers can figure out the mass of the foreground star relative to its planet.
In some cases, however, the foreground object could be a free-floating planet, not a star.
Researchers might then be able to measure the mass of the planet relative to its orbiting companion: a moon. While astronomers are actively looking for exomoons - for example, using data from NASA's Kepler mission - so far, they have not found any.
In the new study, the nature of the foreground, lensing object is not clear. The ratio of the larger body to its smaller companion is 2,000 to 1.
That means the pair could be either a small, faint star circled by a planet about 18 times the mass of Earth - or a planet more massive than Jupiter coupled with a moon weighing less than Earth.
The problem is that astronomers have no way of telling which of these two scenarios is correct.
The answer to the mystery lies in learning the distance to the circling duo. A lower-mass pair closer to Earth will produce the same kind of brightening event as a more massive pair located farther away.
But once a brightening event is over, it's very difficult to take additional measurements of the lensing system and determine the distance.
The true identity of the exomoon candidate and its companion, a system dubbed MOA-2011-BLG-262, will remain unknown, researchers said.