The directed movement of nicotinamide mononucleotide into, out of or within a cell, or between cells, by means of some agent such as a transporter or pore. Nicotinamide mononucleotide is a ribonucleotide in which the nitrogenous base, nicotinamide, is in beta-n-glycosidic linkage with the c-1 position of D-ribose. It is a constituent of NAD and NADP.