I used to have this but i kinda grew over it. But what i hated more was being overheard by people around me. I only picked up my phone when i knew no one heard me.
That was kind of a problem at my first job when i had to answer my phone and others phones when my coworkers were in the same room. But because i was forced to pick it up I got used to it and at some point i really didn't care anymore.
Also there was a girl at my work who had it severely in the beginning too. She had it very bad. She almost went mute and started hyperventilating. But everyone supported her and tried to encourage her to pick up the phone more often. And a couple weeks/months later she sounded like a natural on the phone. Like you couldn't tell she ever had a problem with it. Remarkable.
That kind of made me realise that its alright and many people have this fear. People can relate to it and they will not judge you on it. And to be honest, seeing that girl struggle made me like her more...
I think that if you had to call 1000 people in one day, with people sitting around you, at the end of the day your fear would be gone. If you get a couple nice conversations going it will make you more confident and little by little you'll get over it and see that its not a big deal. It's just when you avoid it, it becomes a big deal in your mind and makes it even harder. I sometimes have a few conversations on the phone that don't really go very smooth and feel a bit awkward, but that happens to everyone.