I just noticed today that my 6th string is making noise without touching it. I never really noticed this before because I figured it was me just playing sloppily, but I was trying really hard to keep string noise down today and no matter what I did I couldn’t stop this mystery noise when picking the second string. Turns out it was the sixth string (which I wasn’t trying to mute because it’s so far away from what I was playing). I know it’s not my palm hitting it or anything because I tested this several times and deliberately picked the second string without touching anything else, and my sixth string started vibrating out of no where! What is up with this? Is it normal or is my guitar set up wrong? Is the only way to stop it by muting my sixth string all the time?
Its pretty typical some strings will catch some of the resonant energy from the others
solution to pretty much anything thats sounding that you dont want sounding is muting it
Engineering world calls this a sympathetic resonance. It is the vibration of one string inducing a vibration in another. It can be the same tone, or a common harmonic point. For instance plucking the small E and muting it will probably leave you hearing the note, but on the big E. Fretting a note on one string can easily set up an open string ringing.
All three of my guitars have this. One is particularly strong. You are likely to find more that the one you found. 
Like Rob says, you will want to plan to mute the string that you want quiet.