It does not appear so, though you should really talk to your attorney.
The statute RCW 9.41.040 lists a number of crimes that make you ineligible to possess a firearm, and malicious mischief 3 is not one of them: http://apps.leg.wa.gov/rcw/default.aspx?cite=9.41.040
There could be other reasons why you might be ineligible to possess a firearm, but a conviction for malicious mischief 3 in Washington State does not appear to be one of them.
You should be fine under the State Statute as MM3 DV is not a crime for which you lose your State firearms rights. If a DV No Contact Order was put in place as part of your conviction, however, you may be prohibited from obtaining a firearm pursuant to 18 USC 922 as there are federal prohibitions under some circumstances where the individual is the restrained party in a DV NCO. I attached a link to the Federal statute for you to review (18 USC 922(g) specifically).
Jeff Holmes - Attorney at Law - firstname.lastname@example.org - 360.975.9288. Disclaimer: This answer does not constitute legal advice. This information is based on general principles of law, as well as my general experience that may or may not relate to your specific situation. This information is not meant to take the place of actually consulting an Attorney in your jurisdiction. If you would like legal advice, I would recommend consulting an attorney in your locale.
I agree with previous answers, but I want to expand upon loss of Federal and State gun rights after a domestic violence charge.
Under Federal Law, 18 U.S.C. § 922(g)(9) prohibits a person who has been convicted of a "misdemeanor crime of domestic violence" from possessing a firearm.
18 U.S.C. § 921(a)(33)(A)(ii) defines "misdemeanor crime of domestic violence" as a misdemeanor under Federal or State law that has, as an element, the use or attempted use of physical force, or the threatened use of a deadly weapon, committed by one family member or member of a household against another.
Malicious mischief in the 3rd degree (RCW 9A.48.090) does not have as an element use of physical force against a person. Rather, malicious mischief is a knowing and malicious act that causes physical damage to the property of another.
So, no loss of Federal gun rights.
Under state law, RCW 9.41.040 prohibits a person convicted of: (1) a "serious offense" (most felonies); or (2) "any of the following crimes when committed by one family or household member against another, committed on or after July 1, 1993: Assault in the fourth degree, coercion, stalking, reckless endangerment, criminal trespass in the first degree, or violation of the provisions of a protection order or no-contact order restraining the person or excluding the person from a residence (RCW 26.50.060, 26.50.070, 26.50.130, or 10.99.040)" from possessing a firearm.
Thus, no loss of State gun rights.