Recently, the use of porous materials has grown widely in many structures, such as beams, plates, and shells. The characteristics of porous materials change in the thickness direction by different functions. This study has investigated the free vibration analysis of a sandwich porous elliptical micro-shell with a magneto-rheological fluid (MRF) core for the first time. Initially, we examined the displacement of the middle layer’s macro- and micro-components, using Love’s shell theory. Next, we used the modified couple stress theory (MCST) to obtain the strain and symmetrical curvature tensors for the three layers. The Hamilton’s principle was implemented to derive the equations of motion. We also used the Galerkin’s method to solve the equations of motion, resulting in a system of equations in the form of a linear eigenvalue problem. By solving the governing equations, we obtained the various natural frequencies and loss factors of the elliptical micro-shell, and compared them with the results in earlier studies. Lastly, we investigated the effects of thickness, porosity distribution pattern, aspect ratio, length scale parameter, and magnetic field intensity on the natural frequency and loss factor of the micro-shell. The data accuracy was validated by comparing them with those of reputable previous articles.