As the number of IoT objects is growing fast, power consumption and security become a major concern in the design of integrated circuits. Lightweight Cryptography (LWC) algorithms aim to secure the communications of these connected objects at the lowest energy impact. To reduce the energy footprint of cryptographic primitives, several LWC hardware implementations embedding hybrid CMOS/MRAM-based cells have been investi- gated. These architectures use the non-volatile characteristic of MRAM to store data manipulated in the algorithm computation. We provide in this work a security evaluation of a hybrid CMOS/MRAM hardware implementation of the ASCON cipher, a finalist of the National Institute of Standards and Technology LWC contest. We focus on a simulation flow using the current EDA tools capable of carrying out power analysis for side-channel attacks, for the purpose of assessing potential weaknesses of MRAM hybridization. Differential Power Analysis (DPA) and Correlation Power Analysis (CPA) are conducted on the post- route and parasitic annoted netlist of the design. The results show that the hybrid implementation does not significantly lower the security feature compared to a reference CMOS implementation.