Muting unused strings when playing power chords

Answer

First of all, you need to work on your picking, making it targeting only the strings a power chord consists of, while avoiding accidental picking of the adjacent strings.

You can mute the adjacent strings by slightly touching them with any part of your available fingers on the fretting hand.

In the following example the index and the pinky finger press the A and D string when performing a power chord, while the middle finger slightly touches the unused low E string, the side of the pinky finger the unused G string.

You can also use your thumb to silence the low E string.

When you transit the fretting hand from one power chord position immediately to the next, without regard if it's on the same or different strings, at the moment the hand takes off from the first chord, it "automatically" stops the strings from ringing, and in the very short interval of time, until you play the next chord there won't be any significant noise.

But if you need to pause before playing the next chord, like here:

the noise will occur, to avoid this, in the breaks between the chords put the edge of your picking hand across the strings, like you do with the palm mute technique.