We present a study of mechanical, electronic and magnetic properties of two-dimensional (2D), monolayer of silicon carbide (SiC) in honeycomb structure and its quasi-one-dimensional (quasi-1D) armchair nanoribbons using first-principles plane-wave method. In order to reveal dimensionality effects, a brief study of three-dimensional (3D) bulk and 1D atomic chain of SiC are also included. Calculated bond-lengths, cohesive energies, charge transfers and band gaps display a clear dimensionality effect. The stability analysis based on the calculation of phonon frequencies indicates that 2D SiC monolayer is stable in planar geometry. We found that 2D SiC monolayer in honeycomb structure and its bare and hydrogen passivated nanoribbons are ionic, nonmagnetic, wide band gap semiconductors. The band gap is further increased upon self-energy corrections. The mechanical properties are investigated using the strain energy calculations. The effect of various vacancy defects, adatoms, and substitutional impurities on electronic and magnetic properties in 2D SiC monolayer and in its armchair nanoribbons is also investigated. Some of these vacancy defects and impurities, which are found to influence physical properties and attain magnetic moments, can be used to functionalize SiC honeycomb structures. © 2010 The American Physical Society.