Summary: In this paper, we construct a generalization of the Kohnen plus space for Hilbert modular forms of half-integral weight. The Kohnen plus space can be characterized by the eigenspace of a certain Hecke operator. It can be also characterized by the behavior of the Fourier coefficients. For example, in the parallel weight case, a modular form of weight \(\kappa + (1/ 2)\) with \(\xi\text{th} \) Fourier coefficient \(c(\xi)\) belongs to the Kohnen plus space if and only if \(c(\xi )= 0\) unless \((-1)^{\kappa }\xi\) is congruent to a square modulo \(4\). The Kohnen subspace is isomorphic to a certain space of Jacobi forms. We also prove a generalization of the Kohnen-Zagier formula.