Hi.
When I play a note, I mute it by lifting my fretting finger while keeping it lightly touching the string. This works fine on most notes.
However, when I do the same thing on the 5th or 7th fret of the A string, or the 7th fret of the D string, I get an extra high-pitched noise instead of a clean mute. The noise gets louder if I turn up the amp’s volume.
Is the noise normal? Any way to solve this?
Thanks.
I believe you’ve discovered harmonics. Jaco Pastorius was pretty famous for playing them. Check this video out for some more info on playing them:
Your the opposite of me. I was actually looking for that noise at first. I had heard things about them. Perfectly normal just harmonics, as your technique improves it will be controlled better.
press a little harder, or softer, as others say - you are pressing just the right amount to cause a harmonic
To stop it you need to move your finger slightly left or right. It is useful if you know how to tune your bass with this method. 5th E harmonic is the same as the 7th A harmonic and so on for the others.
Be “careful” with this video! It’s too advanced for the OP at this stage. Jaco played a lot of “artificial” harmonics, as demoed in the intro. These are very hard to learn, and there is no reason for someone just starting to explore these.
That said, have fun exploring the “natural” harmonics, on the 12th, 7th, 5th (and just below the 4th) frets, respectively.
No need to go all Jaco just yet 
There’s no need for anyone to try to go full-Jaco. 
That would be to dream the impossible dream. 
Well… you know: aim for the stars, shoot for the moon 
Good suggestions, let me offer another. Simply lightly touch the same string with a second finger and the harmonic will not ring out.
I chose that one because it more than talked about it but actually showed playing them and explaining a bit to understand what was happening and OP could determine if that was what they were experiencing or something else.
Moving my finger slightly left works 
Thanks!
Maybe I should practice muting with the ‘sneaky finger’? 
3rd and 9th are also doable. then it’s false harmonic territory, but that’s not accidental 
You may have your fingers curled over the top instead of laying flat across the strings. This is a common thing most beginners do. (I did.) If you keep your fingers flatter, the muting happens sort of automatically.
Video I made for someone else explaining/demonstrating:
