No—photographing the moon, planets, or stars will not damage your camera sensor, and they’re not bright enough to pose the same risk as the sun. The moon is vastly dimmer than direct sunlight, and stars are only tiny points of light, so normal night-sky shooting is safe.

The main practical issue is exposure, not damage: the moon often looks overexposed because it’s bright against a very dark sky, so manual exposure or negative exposure compensation usually works better.

One caveat: extremely long exposures can heat the sensor and increase noise, and in unusual cases prolonged operation could stress older cameras. In practice, it’s better to shoot a series of shorter exposures and stack them later. That also helps reduce noise, and avoids star trails unless you’re using a tracking mount.