The lower part of a bikini without the upper part (i.e., topless).
1965, "Topless Triumph", Time, 12 Mar 1965:
All this so impressed the Appellate Court in Aix-en-Provence that it reversed the convictions. "Inasmuch as the spectacle of the nudity of the human body has nothing intrinsic in it that would outrage normal, even delicate decency, and since Claudine Durand concealed her sexual parts with a sufficiently opaque monokini, we acquit her."
2009, Angelique Crisafis, "France Falls Out of Love with Topless Sunbathing", The Guardian, 22 Jul 09:
French academics and historians have spent the early summer months pondering the sociological meaning of the demise of France's once-favourite piece of beachwear, the "monokini" – the bottom half of a bikini with no top.