The rover, which has been exploring the Red Planet since 2012, discovered a series of ancient riverbeds and deltas in an area called Glen Torridon.
These features suggest that water once flowed from higher ground down into a crater, forming a lake.
The water eventually dried up, leaving behind the riverbeds and deltas that Curiosity has found.
"We're seeing very clear evidence of a river system that flowed into a crater and then filled it up with sediment," said Ashwin Vasavada, Curiosity's project scientist at NASA'S Jet Propulsion Laboratory in Pasadena, California.
The discovery is important because it provides new insights into the history of water on Mars.
Scientists have long believed that Mars was once a much wetter planet than it is today, but the evidence for this has been limited.
Curiosity's findings add to the growing body of evidence that suggests that Mars once had a much different climate than it does today.
"This is a really big deal," said Jim Green, NASA's director of planetary science. "It's the first time that we've seen definitive evidence of a river system on Mars that was active relatively recently in the planet's history."
The discovery also has implications for the search for life on Mars.
If there was once water on Mars, it is possible that there could have been life there as well.
Curiosity's findings raise the hopes that scientists may one day find evidence of past life on Mars.
"This is a very exciting discovery that opens up new possibilities for the exploration of Mars," said NASA Administrator Jim Bridenstine. "We can't wait to see what else Curiosity finds in the years to come."
