In this paper, the analogue of electromagnetically induced transparency is achieved in a magnetic metamaterial consisting of coupled “radiative” square closed loop (SCL) and “dark” square spiral resonator (SSR). Full-wave numerical simulations are carried out to validate the EIT-like effect of the magnetic metamaterial. Transmission spectrums and surface current distributions for the metamaterial are presented. It is shown that placing the SSR close to the SCL causes the electromagnetic field energy to be coupled back and forth between them. This leads to destructive interference and the transparency window in the transmission stop-band of the metamaterial. In addition, it is numerically demonstrated that the magnetic metamaterial can be employed as a refractive-index based sensor with a sensitivity of 41.3 mm/RIU, which means that the resonance wavelength of the sensor shifts 41.3 mm per unit change of refractive-index of the surrounding medium.