We present spectroscopic follow-up observations of galaxies from the Munich Near-Infrared Cluster Survey ( MUNICS ) . MUNICS is a wide-field medium-deep K ^ { \prime } -band selected survey covering 1 square degree in the near-infrared K ^ { \prime } and J pass-bands , and 0.35 square degrees in I , R , V , and – recently completed – B . The spectroscopic sample comprises observations of objects down to a limit of K ^ { \prime } \leq 17.5 in five survey fields ( 0.17 square degrees in total ) , and a sparsely selected deeper sample ( K ^ { \prime } \leq 19.0 ) constructed in one of the survey patches ( 0.03 square degrees ) . Here we describe the selection procedure of objects for spectroscopic observations , the observations themselves , the data reduction , and the construction of the spectroscopic catalogue containing roughly 500 galaxies with secure redshifts . Furthermore we discuss global properties of the sample like its distribution in colour-redshift space , the accuracy of redshift determination , and the completeness function of the data . We derive the rest-frame K ^ { \prime } -band luminosity function of galaxies at median redshifts of z = 0.2 , z = 0.4 , and z = 0.7 . We find evidence for mild evolution of magnitudes ( \Delta M _ { K } ^ { * } \simeq - 0.70 mag ) and number densities ( \Delta \Phi _ { K } ^ { * } / \Phi _ { K } ^ { * } \simeq - 0.35 ) to redshift one . Furthermore , we present the rest-frame J -band luminosity function of galaxies at these redshifts , the first determination of this quantity at higher redshifts , with a behaviour similar to the K -band luminosity function .