The architectural framework plays a major role in determining the optical properties of left-handed materials. Most metamaterial so far designed have been based on complicated resonant elements such as split rings and hyperbolic metamaterials. Unfortunately, magnetic response of most of the materials tails off at higher frequencies. Higher frequency excitation in metamaterials requires more complicated designs or toroidal moment. In the proposed magnonic metamaterials, the toroidal excitations are naturally maintained and make it suitable for THz resonances. Magnetism and left-handed behavior are the two extreme phenomena that do not seem to be compatible and the coexistence of both cooperative effects was not foreseen. Terahertz spintronics is an emerging field that bridges the boundary between magnetism and photonics, which make the magnetic material suitable for photonic applications. Here, we present the first numerical realization of a magnonic metamaterial artificial spin ice (ASI), designed to operate at terahertz frequency. The two-dimensional square arrays exhibit a rich spin wave band structure that is tunable both by external electromagnetic fields and the magnetization configuration of individual elements. The ultrafast spin wave resonances have provided a direct gateway to manipulate magnetic field of free-space terahertz pulses. The proposed system consists of two-dimensional square arrays of cobalt nanoislands in four different geometries and the micromagnetic simulations of these systems are carried out using mumax3. From the numerical results, the theoretical prediction of negative permeability is done using Schloemann model.