The growth and electrical characterization of the heterojunction formed between two-dimensional (2D) layered p-molybdenum disulfide (MoS2) and nitrogen-doped 4H silicon carbide (SiC) are reported. The integration of 2D semiconductors with the conventional three-dimensional (3D) substrates could enable semiconductor heterostructures with unprecedented properties. In this work, direct growth of p-type MoS2 films on SiC was demonstrated using chemical vapor deposition, and the MoS2 films were found to be high quality based on x-ray diffraction and Raman spectra. The resulting heterojunction was found to display rectification and current-voltage characteristics consistent with a diode for which forward conduction in the low-bias region is dominated by multi-step recombination tunneling. Capacitance-voltage measurements were used to determine the built-in voltage for the p-MoS2/n-SiC heterojunction diode, and we propose an energy band line up for the heterostructure based on these observations. The demonstration of heterogeneous material integration between MoS2 and SiC enables a promising new class of 2D/3D heterostructures.