Considerable interest to magnetism of MnAs both in bulk or in the form of epitaxial films is stimulated by its applications as a magnetocaloric material and in spintronic devices. Since the MnAs films deposited on GaAs reproduce well a magnetic transformation related to α–β magnetostructural transition that occurs in bulk MnAs, this first-order phase transition occurs through a phase coexistence over a wide temperature range. Here, we considered the same magnetostructural transition in a bulk hybrid structure based on micrometer-scaled MnAs inclusions embedded into the Cd3As2 matrix. In particular, the effect of high pressure and magnetic fields on the ferromagnetic transition temperature, TC, in a composite Cd3As2 + 30 mol. % MnAs has been studied. We found that at ambient pressure, the transition from α-MnAs to β-MnAs is accompanied by the absence of thermal hysteresis of magnetization, implying a phase coexistence regime. The hysteresis width does not markedly increase even at pressures about P = 0.35 GPa, and displacement of TC occurs with a rate of dTC/dP ∼ −91.42 K/GPa. In the temperature region of the α–β phase coexistence, a local peak at T = 283 K and P = 1 GPa is observed, which is associated with an antiferromagnetic order of MnAs inclusions. Direct measurements of isothermal magnetization vs pressure indicate both the stabilization of the ferromagnetic hexagonal α phase at P < Pmax and the development of an orthorhombic antiferromagnetic long-range order, which propagate up to 5 GPa.