Our aim in this paper is to give a Gagliardo-Nirenberg inequality for generalized Riesz potentials Iρ,µ,κf of functions in Musielak-Orlicz spaces over quasimetric measure spaces, as an extension of work of Mizuta et al. (2012). What is new in this paper is that ρ depends on (Formula Presented) and that the underlying measure µ is not doubling.