Quantum computers may offer significant computational advantages over classical counterparts, revolutionizing the technology landscape in the near future. When networked together, the advantage of quantum computing may be further amplified, and there may emerge innovative applications. Among various active explorations on distributed quantum computing, multiqubit quantum gates between distant networked quantum computers are of particular interest because they offer operational advantages of efficiency and fidelity. Here we report the first experimental demonstration of quantum teleportation for a Toffoli gate, which is a commonly used multiqubit quantum gate, across three spatially distributed parties within a photonic quantum network. Employing the Hofmann method, we estimate the fidelity of the teleported Toffoli gate to be at least 0.706 ± 0.131. This successful demonstration of the quantum teleportation of a Toffoli gate constitutes a critical step toward the ultimate realization of distributed quantum computation.