In many countries, Jerusalem artichoke (JA) is a source of biomass for renewable energy production and alternative biofuel feedstock, and it is used for feed and food production. The species also has medicinal properties, and it is used in soil reclamation. The aim of this study was to evaluate the effect of N fertilization on the yield and macronutrient concentrations in JA tubers. The effect of N fertilization (control plot, unfertilized, 80 and 120 kg ha−1) on aerial biomass yield, tuber yield, and the mineral composition of tubers in three JA cultivars (“cv.”) (Rubik, Albik, and Gute Gelbe) was investigated in a field experiment. Tuber yield (40.99 Mg ha−1) and aerial biomass yield (62.76 Mg ha−1) were highest in cv. Gute Gelbe fertilized with 120 kg N ha−1 in the warm and moderately wet growing season of 2018. Agronomic N-use efficiency (AE) was highest in cv. Gute Gelbe. In the treatment supplied with 80 kg N ha−1, the fresh matter yield (FMY) of tubers was determined at 66.4 kg kg−1 N, whereas in the treatment fertilized with 120 kg N ha−1, the FMY of tubers reached 101.8 kg kg−1 N. The evaluated JA cultivars differed in their responses to an increase in the N fertilizer (marginal efficiency—ME) rate from 80 to 120 kg ha−1. The strongest response was observed in cv. Gute Gelbe, where the tuber yield increased by 172.6 kg kg−1 N. The tubers of cv. Gute Gelbe were characterized by significantly higher concentrations of N, K, Mg, and S compared with the other cultivars. The concentrations of macronutrients in the tubers (without Mg) were higher in spring. Nitrogen fertilization did not cause differences in the concentrations of P, K, Ca, Mg, and S, but it increased the N concentration in tubers.