This is normal. It is calledThe problem caused by "sympathetic resonance." On any string instrument, the strings actually cause the whole instrument to resonate. So, the vibration of the higher strings is activating those lower strings as well.
Some instruments (like the sitar) are designed specifically to enhance these sympathetic resonances, but if you don't want the lower strings to resonate, you will need to mute them with either your left-hand fingers or right-hand palm.
If the sound is unpleasant, though, you should take it to a guitar tech, so they can take a look at it.