We report the rhythmic growth and disappearance of a micrometer-sized water droplet under stationary nonequilibrium conditions, with a periodicity of similar to 1 s. Under a supersaturated vapor, a micro water droplet nucleates on a glass plate, grows and then disappears when the growing droplet touches a larger water sink, and this cycle repeats in a rhythmic manner. We discuss the rhythmic phenomenon as a kind of limit cycle oscillation.