Axion dark matter may induce observable electromagnetic effects in resonant cavity systems, and potentially lead to modifications of the Casimir interaction. In this context, graphene represents a particularly attractive platform owing to its distinctive and tunable electromagnetic properties, and the fact that its electromagnetic response can be modelled microscopically from first principles within quantum field theory. The electromagnetic response induced by axion dark matter is investigated in a planar cavity geometry consisting of parallel graphene interfaces in the presence of a homogeneous external magnetic field, incorporating finite temperature, chemical potential and dissipation effects through the graphene conductivity. Closed analytical expressions are obtained for the induced electric field and the resulting pressure exerted on the interfaces. The pressure exhibits resonant enhancement, at a series of plate separations satisfying d_n = [2πn- ϕ(r)]/m_a, where ma is the axion mass and the phase ϕ(r) is determined by the reflection coefficient r, which depends on the graphene conductivity evaluated at the axion frequency ω = m_a. The resonant structure is strongly influenced by the graphene chemical potential and damping parameter. In particular, increased doping, for example via a gate voltage, sharpens the resonances and amplifies the axion-induced signal. By comparing the resonantly enhanced signal with the conventional Casimir background, the parametric regimes in which the effect could become experimentally relevant are identified, with the strongest sensitivity obtained for highly doped low-dissipation graphene configurations operated near resonance. These results demonstrate that graphene-based Casimir-type configurations may provide a sensitive framework for probing axion-induced electromagnetic phenomena and highlight the interplay between axion electrodynamics, cavity resonances, and material properties in low-dimensional systems.