$^{11}B$ nuclear magnetic resonance (NMR) measurements have been performed to investigate electronic structures and vortex states of $M_gB_2$ superconductor. The central transition shows a narrow peak down to 25 K at 3.15 T. Below 25 K, an extra line starts to show up and dominates. The extra line is broad and asymmetric with a long tail in the high frequency side, which confirms that this originates from vortex pinning below the irreversibility temperature. From temperature evolution of the fraction and linewidth of the broad portion, temperature dependence of coherence length and penetration depth are extracted.