There was "a vigorous flow on the surface of Mars," said chief scientist John Grotzinger of the California Institute of Technology. "We're really excited."
Present-day Mars is a frozen desert with no hint of water on its surface, but geological studies of rocks by previous missions suggest the planet was once warmer and wetter.
The latest evidence came from photos that Curiosity took revealing rounded pebbles and gravel -- a sign that the rocks were transported long distances by water and smoothed out.
It is unclear how long the water persisted on the surface, but it easily could have lasted "thousands to millions of years", said mission scientist Bill Dietrich of the University of California, Berkeley.
Finding past water is a first step towards learning whether the environment could have supported microbes.
While an ancient streambed holds promise as a potentially habitable environment, scientists do not think it is a good place to preserve the carbon building blocks of life. That's why Curiosity will continue its trek to where there is a better chance of finding organics.