(1) Background: In recent years, the use of light emitting diodes (LEDs) for plant production purposes has expanded. However, LEDs’ effect on seed germination and early seedling growth has been scarcely documented. (2) Methods: In this work, the effect of monochromatic red light (RL, 100 µmol m−2 s−1) for up to 60 min applied to seeds of pea and melon was analyzed in terms of seedling growth and antioxidant enzymes levels. An experimental LED chamber coupled to an electronic control system was developed for this purpose. (3) Results: RL did not alter the germination rate, but significantly improved the early seedling growth. Pea and melon seedlings showed the highest increase in fresh weight and length upon 15 min RL treatment of the seeds, whereas longer exposure times decreased seedling growth. Interestingly, RL favored the development of secondary roots in both species, which could favor the nutrition and water uptake by the seedling. The ability of the seedlings to respond to a hypothetical LED irradiance-induced oxidative stress was reflected differently on the antioxidant system of pea and melon. (4) Conclusions: These findings can be relevant for designing seed priming treatments to improve plant vigor, thus enhancing the productivity of important crop plants.