Background: Mounting epidemiological evidence suggests an association between prenatal tobacco exposure and an increased risk of tobacco smoking in offspring. However, it is uncertain whether the association is due to the intrauterine or shared environmental exposures. Methods: Study participants were from the Raine Study, a prospective birth cohort study based in Perth, Western Australia (N = 2730). Tobacco smoking in adolescents, at age 17 years, was measured using a self-reported questionnaire. Log-binomial regression was used to estimate the relative risks (RRs) of tobacco smoking in offspring exposed to maternal prenatal tobacco use during the first and third trimesters of pregnancy. We have also calculated the E-values to investigate the potential effect of unmeasured confounding. Paternal smoking during pregnancy was used as a negative control for comparison. Results: A total of 1210 mothers-offspring pairs were included in the final analysis. After controlling for potential confounders, we found increased risks of tobacco smoking in offspring exposed to maternal prenatal tobacco use during the first trimester [RR 1.50 (95% CI: 1.13–1.97)] (E-value for point estimate = 2.37) and during both trimesters of pregnancy [RR 1.41 (95% CI: 1.03–1.89)] (E-value for point estimate = 2.17). However, we found insufficient statistical evidence for an association between paternal smoking during pregnancy and risk of tobacco smoking in offspring [RR 1.18 (95% CI: 0.84–1.67)]. Conclusion: Maternal prenatal tobacco exposure was associated with an increased risk of tobacco smoking in offspring at the age of 17 years. Tobacco smoking cessation at the early stages of gestation may reduce the risk of tobacco smoking in the next generation.