It is necessary to develop new energy technologies because of serious environmental problems. As one of the most promising electrochemical energy conversion and storage devices, the Zn–air battery has attracted extensive research in recent years due to the advantages of abundant resources, low price, high energy density, and high reduction potential. However, the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) of Zn–air battery during discharge and charge have complicated multi-electron transfer processes with slow reaction kinetics. It is important to develop efficient and stable oxygen electrocatalysts. At present, single-function catalysts such as Pt/C, RuO2, and IrO2 are regarded as the benchmark catalysts for ORR and OER, respectively. However, the large-scale application of Zn–air battery is limited by the few sources of the precious metal catalysts, as well as their high costs, and poor long-term stability. Therefore, designing bifunctional electrocatalysts with excellent activity and stability using resource-rich non-noble metals is the key to improving ORR/OER reaction kinetics and promoting the commercial application of the Zn–air battery. Metal–organic framework (MOF) is a kind of porous crystal material composed of metal ions/clusters connected by organic ligands, which has the characteristics of adjustable porosity, highly ordered pore structure, low crystal density, and large specific surface area. MOFs and their derivatives show remarkable performance in promoting oxygen reaction, and are a promising candidate material for oxygen electrocatalysts. Herein, this review summarizes the latest progress in advanced MOF-derived materials such as oxygen electrocatalysts in a Zn–air battery. Firstly, the composition and working principle of the Zn–air battery are introduced. Then, the related reaction mechanism of ORR/OER is briefly described. After that, the latest developments in ORR/OER electrocatalysts for Zn–air batteries are introduced in detail from two aspects: (i) non-precious metal catalysts (NPMC) derived from MOF materials, including single transition metals and bimetallic catalysts with Co, Fe, Mn, Cu, etc.; (ii) metal-free catalysts derived from MOF materials, including heteroatom-doped MOF materials and MOF/graphene oxide (GO) composite materials. At the end of the paper, we also put forward the challenges and prospects of designing bifunctional oxygen electrocatalysts with high activity and stability derived from MOF materials for Zn–air battery.