Considering the serious risks posed by the heavy metals present in pig diets, monitoring and controlling the amount of these metals is crucial. The laser-induced breakdown spectroscopy (LIBS) is a promising technique for performing elemental analysis due to its unique advantages, such as rapid, in situ, nondestructive, and online detection of various minerals. In order to improve the detection accuracy and detection limit (LOD) of elements, the spatial constraint combined with laser-induced breakdown spectroscopy (CC-LIBS) is used to detect the quantity of zinc in pig feed and achieve the detection of samples with lower concentrations. Zn I 480.86 nm is selected as the characteristic spectral line, and the effects of different two-dimensional (cylindrical) and three-dimensional (hemispherical, truncated cone) cavities on the enhancement factor are compared under different time delays. The results show that the optimal conditions include a truncated cone cavity D5H3, a delay time of 2.08, and an enhancement factor of 3.01 associated with the analytical spectral line. The detection limit of zinc in samples under CC-LIBS is 62.67 mg/kg (the recommended quantity of zinc in pig diet mentioned in the safe use of feed additives is 43–80 mg/kg), which is 35.65% lower than that under the LIBS (97.39 mg/kg). Therefore, this work provides a new test basis and idea for the detection of zinc in pig feed.