Origami inspires various designs of foldable prismatic structures with zero-thickness facets. However, there is a difficulty in directly applying them to thick materials. This paper presents a novel design of the foldable prismatic structure inspired by the zigzag pattern, which can accommodate the thickness of materials easily by placing hinges on the top or bottom surfaces of panels. The foldable prismatic structures are constructed by connecting multiple zigzag strips, in which each strip is made up of uniform-thickness hexagonal panels. By identifying the relationship between the foldable structure and spatial linkages, we analyze the mobility of the assembly based on the matrix method with DH notations. The result reveals that the foldable prismatic structure is equivalent to a network of spherical 4R linkages and Bennett linkages, and its motion has a single-degree-of-freedom. Based on the proposed foldable prismatic structure, a foldable manipulator is developed to demonstrate its potential engineering applications. The actuation strategy is designed by employing a motor-cable-driven system and torsional spring hinges. The physical prototype of the foldable manipulator is fabricated, and experimental results prove that our designs are feasible and effective.