Pregnancy during adolescence is associated with adverse birth outcomes, including preterm delivery and low birthweight. The nutrient availability to the fetus may be limited if the mother is still growing. This research aims to study the effects of pregnancy during adolescence in a nutritionally poor environment in rural Nepal. This study utilized data from a randomized controlled trial of micronutrient supplementation during pregnancy in south-eastern Nepal. Women of parity 0 or 1 and of age ≤ 25 years who gave birth to a singleton liveborn infant who was measured within 72 h of delivery were included (n = 1393). There was no difference in the risk of low birthweight (OR = 0.96; 95% CI = 0.90–1.02) or small for gestational age (OR = 1.01; 95% CI = 0.94–1.08) per year of increasing maternal age among primiparae. Young maternal age did not affect the anthropometry or gestational age of the offspring of parity 1 women. Each year of increasing maternal age among primiparae was associated with increases in birth length (0.07 cm; 95% CI = −0.01 to 0.16), head (0.05 cm; 95% CI = 0.01–0.09) and chest circumference (0.07 cm; 95% CI = 0.01–0.12), but not weight (9.0 g; 95% CI = −2.1 to 21.8) of their offspring. Young maternal age was associated with an increased risk of preterm delivery among primiparae (OR = 2.07; 95% CI = 1.26–3.38) that occurred at an age cut-off of ≤18 years relative to those 19–25 years. Thus, we conclude that young maternal age (≤18 years) increased the risk of preterm delivery, but not intrauterine growth retardation, for the first but not second liveborn infant.