Corresponding to a hypergraph G with d vertices, a quantum hypergraph state is defined by vertical bar G > = 1/root 2(d) Sigma(2d)(n=0) (1)(-1)(integral(n)) vertical bar n >, where f is a d-variable Boolean function depending on the hypergraph G, and vertical bar n > denotes a binary vector of length 2(d) with 1 at the nth position for n = 0, 1,... (2(d) - 1). The nonclassical properties of these states are studied. We consider the annihilation and creation operator on the Hilbert space of dimension 2(d) acting on the number states \{vertical bar n > : n = 0, 1,... (2(d) - 1)\}. The Hermitian number and phase operators, in finite dimensions, are constructed. The number-phase uncertainty for these states leads to the idea of phase squeezing. We establish that these states are squeezed in the phase quadrature only and satisfy the Agarwal- Tara criterion for nonclassicality, which only depends on the number of vertices of the hypergraphs. We also point out that coherence is observed in the phase