Devices capable of deterministically manipulating the photonic entanglement are of paramount importance, since photons are the ideal messengers for quantum information. However, due to the non-interacting nature of photons, many photonic quantum operations have only been demonstrated using probabilistic linear-optical approaches, which lead to overwhelming resource overhead and poor scalability. Here, we report a novel entanglement filter that transmits the desired photonic entangled state and blocks the unwanted ones. In contrast to prior probabilistic approaches, our experiment exploits strong and controllable photon-photon interaction enabled by Rydberg atoms, so the filtering of undesired states succeeds in a fully deterministic way. Photonic entanglement with near-unity fidelity can be extracted from an input state with an arbitrarily low initial fidelity. The protocol is inherently robust, and succeeds both in the Rydberg blockade regime and in the interaction-induced dissipation regime. Such an entanglement filter opens new routes toward scalable photonic quantum information processing with multiple ensembles of Rydberg atoms.