It's not easy to be absolutely sure but I think the first use of a similar term was by Jack Binder. He coined the term [zero-gravity](http://www.jessesword.com/sf/view/1490) in an article published in ["Thrilling Wonder Stories"](https://www.isfdb.org/cgi-bin/pl.cgi?61747+c) in 1938, but it referred to the absence of apparent gravity at the center of the Earth.

I think the first modern use of [zero-g](http://www.jessesword.com/sf/view/142) was in the 1952 novel ["Islands in the Sky"](https://en.wikipedia.org/wiki/Islands_in_the_Sky) by the late, great Arthur C. Clarke. But someone could have use the term earlier and I just don't know about it.