Experimental investigations have been conducted for the nonlinear dynamical response of a parametrically excited clamped–clamped beam with a central magneto-rheological elastomer (MRE) patch. Experiments have been conducted when the MRE patch was in the absence or presence of an external magnetic field, when the system was parametrically excited either near the fundamental resonance or in the vicinity of the principal parametric resonance; frequency–responses and acceleration-responses were constructed. An electrodynamic shaker parametrically excited each system and the corresponding displacement of the centre of the beam was measured. It has been found that at the fundamental resonance, each system (in the absence or presence of a magnetic field) displays linear behaviour with an internal resonance; however, at the principal parametric resonance a strong softening-type nonlinearity was observed when there was no externally applied magnetic field to the MRE patch—with increasing magnetic field applied to the MRE patch, the principal parametric resonance displayed a weaker nonlinear behaviour. It has been shown that the MRE patch in the absence or presence of an externally applied magnetic field has a substantial quantitative and qualitative effect on the nonlinear dynamical behaviour of the parametrically excited systems.