Hi Joe,
Could you describe the sound?
I'm guessing it may be residual vibrations on the string as you lift up. Do you strings feel sticky, or not smooth? It's possible that your strings are old and you may need to change them. Older strings can feel a little sticky, or just not as smooth as it should be.
Another issue could be that your string height is a bit too high and your fingers are bumping into other strings.
Remember, there's always a little bit of noise when you remove or place your fingers on the fretboard, but if it's very loud and apparent, it may be another issue.
I suggest changing the strings, and adjusting the string height, maybe lowering them or even raising it, until it feels good, and sounds good.
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