Indoor farming is an increasingly popular approach for growing leafy vegetables, and under this production system, artificial light provides the sole source (SS) of radiation for photosynthesis and light signaling. With newer horticultural light-emitting diodes (LEDs), growers have the ability to manipulate the lighting environment to achieve specific production goals. However, there is limited research on LED lighting specific to microgreen production, and available research shows that there is variability in how microgreens respond to their lighting environment. The present study examined the effects of SS light intensity (LI) on growth, yield, and quality of kale (Brassica napus L. ‘Red Russian’), cabbage (Brassica oleracea L.), arugula (Eruca sativa L.), and mustard (Brassica juncea L. ‘Ruby Streaks’) microgreens grown in a walk-in growth chamber. SS LEDs were used to provide six target photosynthetic photon flux density density (PPFD) treatments: 100, 200, 300, 400, 500, and 600 μmol·m−2·s−1 with a photon flux ratio of 15 blue: 85 red and a 16-hour photoperiod. As LI increased from 100 to 600 μmol·m−2· s−1, fresh weight (FW) increased by 0.59 kg·m−2 (36%), 0.70 kg·m−2 (56%), 0.71 kg·m−2 (76%), and 0.67 kg·m−2 (82%) for kale, cabbage, arugula, and mustard, respectively. Similarly, dry weight (DW) increased by 47 g·m−2 (65%), 45 g·m−2 (69%), 64 g·m−2 (122%), and 65 g·m−2 (145%) for kale, cabbage, arugula, and mustard, respectively, as LI increased from 100 to 600 μmol·m−2· s−1. Increasing LI decreased hypocotyl length and hue angle linearly in all genotypes. Saturation of cabbage and mustard decreased linearly by 18% and 36%, respectively, as LI increased from 100 to 600 μmol·m−2·s−1. Growers can use the results of this study to optimize SS LI for their production systems, genotypes, and production goals.