No. You don't. There are professional critics out there who have never touched an instrument or know anything about the music process, but make a living out of it. It certainly does help if you are a musician since you can bring more to to table if you do have knowledge of certain instruments, the recording process or whatever else. But to me, it's more important to have a good ear, an open mind, be unbiased and be good at writing so you can explain your opinion in a logical and engaging way.
As a musician myself, I do find that the knowledge I have picked up over the years come into play when reviewing music. In general i get a greater sense of appreciation for music since I can recognize technical ability, good composition, good songwriting and good sound production. It allows you to recognize when all of these things are correctly executed, when they are not, or when and what individual aspects are. However in the end, what constitutes as good or bad music in a review, does come down to a matter of opinion.