The surface excitation spectra of the B-terminated and Mg-terminated MgB₂(0001) surfaces are studied in the ab initio time-dependent density functional theory approach. The band structure of both these surfaces is fully included into evaluation of the surface response function using a linear response approach. We find that different surface electronic structures for these surface terminations result in very different surface collective electronic excitations. Due to a number of surface states and peculiarity of the MgB₂ dielectric properties several surface plasmons, such as surface plasmon, interband surface plasmon, acoustic surface plasmon, and others have been found. We trace their evolution with momentum transfer change on both surfaces. Whereas at vanishing momentum transfers the plasmons in both systems can be understood considering the bulk MgB₂ dielectric function, upon momentum increase the collective excitations present very different behavior. We relay such behavior to the differences in the surface electronic structure of the studied terminations.