I agree with the consensus here that the description sounds more like a tuning issue than anything. If you have it tuned to the ring, you might try loosening it up just a tad as one mentioned, or maybe dampening it a little as other have suggested.
But more on the point of compression, first of all, yes indeed a compressor can change the sound balance of the instrument.
If the threshold is set above the level of the meat of the pre-compressed ringing and the ratio is set heavy enough to provide several dB of reduction, what can happen is that the dynamic range between the energetic attack and decay frequencies and the lesser sustained ringing is reduced; i.e. most of the non-ringing energy is dropped in amplitude while the amplitude of the ringing has not changed. Then when you apply the output/makeup gain to bring the overall post-compression levels back up, you're just bringingthe non-ringing back to where it was, but you are increasing the level of the ringing several dB above where it originally was. The end effect is a relative boost in the ringing.
Additionally, if much of the ringing is in the envelope's release, slower compression release times can cause the ringing to sustain longer and be more readily audible.
I'd recommend double-checking the tuning first and checking for ringing before compression. Damping is also an option, but like RAK says, if it doesn't sound like it needs damping pre-compression, you should usually be able to avoid it post compression.
I'd try Farview's troubleshooting recipe mentioned above second, with the descriptions I just gave in mind as you t'shoot the compression sound.
If all of that fails and you can't mic it any better to get rid of it, a last-ditch effort may be to look for the fundamental and harmonics of the ringing with an RTA, and then attacking them with a harmonic filter (or series of paraEQ notches if you don't have a paraEQ plug with a harmonic filter setting.)
YMMV, YADAYADAYADA
G.