Solid-state qubits with a photonic interface is very promising for quantum networks. Color centers in silicon carbide have shown excellent optical and spin coherence, even when integrated with membranes and nanostructures. Additionally, nuclear spins coupled with electron spins can serve as long-lived quantum memories. Pioneering work previously has realized the initialization of a single nuclear spin and demonstrated its entanglement with an electron spin. In this Letter, we report the first realization of single-shot readout for a nuclear spin in SiC. We obtain a deterministic nuclear spin initialization and readout fidelity of 94.95% with a measurement duration of 1 ms. With a dual-step readout scheme, we obtain a readout fidelity as high as 99.03% within 0.28 ms by sacrificing the success efficiency. Our Letter complements the experimental toolbox of harnessing both electron and nuclear spins in SiC for future quantum networks.