An instrument on the six-wheeled robot identified mysterious spikes of methane that cannot easily be explained by geology or organic material transported to the planet by comets or asteroids.
While scientists cannot be sure what is producing the methane, they acknowledge the source could be bacteria-like organisms.
If the existence of living, breathing microbes on Mars is confirmed, it will be one of the most monumental discoveries in history.
Previous satellite observations have detected unusual plumes of methane on the planet, but none as extraordinary as the sudden “venting” measured at Gale Crater, where evidence suggests water once flowed billions of years ago.
Curiosity, one of Nasa’s two Mars Exploration Rovers, landed in the 96 mile-wide crater in August 2012 and has been exploring the region since.
Last year Nasa reported that Gale contained the remains of an ancient freshwater lake where there may have been a hospitable environment for life in the distant past.
The new discovery, reported in the journal Science, followed studies of gas samples by Curiosity’s Tunable Laser Spectrometer (TAS), an instrument that uses intense light to carry out chemical analysis.
It revealed a low background level of methane which spiked 10-fold over a period of just 60 Martian days.
In four sequential measurements, Curiosity showed the methane level soaring from about 0.69 parts per billion by volume (ppbv) to 7.2 ppbv.
The spikes occurred within 200 to 300 metres of each other and less than a kilometre from where the lower readings were detected.
By the time Curiosity had travelled a further kilometre, the higher methane levels had disappeared.
In their paper, the US scientists led by Dr Chris Webster, from Nasa’s Jet Propulsion Laboratory in Pasadena, California, wrote: “The persistence of the high methane values over 60 sols (Martian days) and their sudden drop 47 sols later is not consistent with a well-mixed event, but rather with a local production or venting that, once terminated, disperses quickly.”
The wind direction indicated a source to the north of the rover.
Life is the chief producer of methane on Earth, but there are many non-biological processes that can also generate the gas.
The low background level of methane detected by Curiosity can be explained by the Sun’s rays degrading organic material possibly deposited by meteors, said the Nasa scientists.
But the spikes of methane required an additional source, which was unlikely to be a recent impact by comet or asteroid. Such an object would have had to measure several metres across and would have left a large crater, no sign of which was visible.
The short time-scale of the methane spikes did not suggest that the gas was released from volcanic deposits trapped in ice, called clathrates. Nor did it appear to come from the release of gaseous methane that had become bound to the soil.
The Nasa authors are cautious about jumping to conclusions, but conclude that “methanogenesis” - the formation of methane by microbial bugs known as methanogens - may be one answer to the riddle.
They wrote: “Our measurements spanning a full Mars year indicate that trace quantities of methane are being generated on Mars by more than one mechanism or a combination of proposed mechanisms - including methanogenesis either today or released from past reservoirs, or both.”
Gale Crater, on the Martian equator, was created when a large meteor struck the planet 3.5 billion to 3.8 billion years ago.
At its centre is a high mountain, named Mount Sharp, that rises 18,000ft above the crater floor. Flowing water appears to have carved channels in the sides of the mountain and the crater walls.
Another major discovery by Curiosity was that of water bound in the fine-grained soil within the crater. Each cubic foot of Martian soil was found to contain around two pints of water, not freely accessible but attached to minerals.
The rover has reached the base of Mount Sharp and over the coming months will begin a slow climb. Scientists are especially keen to explore the mountain because its sedimentary layers provide tantalising snapshots of Martian history.
The question of whether there is, or was, life on Mars may finally be answered by the European Space Agency’s ExoMars mission, which will land a 300kg rover on the Red Planet in 2019.
ExoMars will be equipped with a two-metre drill and the ability to detect biomarkers of life. It will not be heading for Gale Crater, however. Because it will land with less precision than Curiosity, the crater and its mountain are considered too potentially hazardous.