If confirmed, the "exomoon" is likely to be about the size and mass of Neptune, and circles a planet the size of Jupiter but with 10 times the mass.
The signal was detected by Nasa's Kepler Space Telescope; astronomers now plan to carry out follow-up observations with Hubble in October.
A paper about the candidate moon is published on the Arxiv pre-print site.
To date, astronomers have discovered more than 3,000 exoplanets - worlds orbiting stars other than the Sun.
A hunt for exomoons - objects in orbit around those distant planets - has proceeded in parallel. But so far, these extrasolar satellites have lingered at the limits of detection with current techniques.
Dr David Kipping, assistant professor of astronomy at Columbia University in New York, says he has spent "most of his adult life" looking for exomoons.
For the time being, however, he urged caution, saying: "We would merely describe it at this point as something consistent with a moon, but, who knows, it could be something else."
The Kepler telescope hunts for planets by looking for tiny dips in the brightness of a star when a planet crosses in front - known as a transit. To search for exomoons, researchers are looking for a dimming of starlight before and after the planet causes its dip in light.