Other than the obvious "take your fingers off the strings when shifting" advice, you can't really stop it completely. Sound is going to be made when there is friction. Muting strings is something you need to learn, but even a dead/muted string will make noise from running your fingers back and forth.

As long as it is a dead/muted sound, it's kind of normal. If the strings are ringing out then you need to mute better.