Absolutely not. Although there's an argument to be made that production is its own kind of musicianship...
Most famous producers aren't performing professional musicians, and that's partly because the mindset is so different. As a pro musician, you worry about technique and executing the music live. As a pro producer, you're not worried about technique and execution, you're worrying about getting a great sound. You wouldn't be worried about nailing the rhythms down perfectly so much as you would be worried about keeping the mix from being muddy.
With zero musical knowledge, being a producer would be difficult. A basic level of musicianship can be a strong tool, since the end result is still music, but by no means do you need to be a Carnegie Hall pianist to put some keys in your EDM track.
I definitely think continuing to practice the instruments you play will be helpful to you, but you probably don't need to concern yourself with being a pro-level instrumentalist. In fact, it's quite common for instruments to be programmed into produced music, where the producer would write the part and the computer would execute it in the song. A knowledge of instruments is helpful for writing those parts, but not strictly necessary.
Composers usually don't play every instrument that they write for at the professional level, and in fact often can write parts for instruments they have never played, simply because they know the sound of that instrument so well. The same is true of producers; if you know the sound of what you want well and have it internalized, you can produce good music.