Background: The prevalence of low birth weight (LBW) is a major public health issue in India; however, the optimal growth pattern for such infants is not clear. The purpose of this study is to understand the causal association between LBW and stunting of preschool children in India. Methods: The National Family Health Survey-4 is a large cross-sectional survey based on a nationally representative sample of 699,686 women in the age group of 15–49 years and was conducted during 2015–2016 in India. The study used the children’s file with a sample of 259,002 of 0–59 months for investigation. Results: The data revealed that 38.7% of the children in India were stunted. The bivariate analysis revealed that, of the women who did not attend any antenatal care (ANC) meetings, 46.8% had stunted children compared to the women who attended more than three ANC meetings, which 30.7% had stunted children. The low birth weight children experienced a much higher chance of stunting compared to children with a normal birth weight (44.3% vs. 33.8%). The multivariable odds ratios of logistic regression, after adjusting for the confounding characteristics, showed that pregnant women attending more than three ANC meetings compared to not attending any ANC meetings experienced a 19% lower adjusted odds ratio (AOR) of having stunted children (AOR = 0.81; CI 0.78, 0.85; p < 0.001). Another important variable, such as women with underweight body mass index (BMI) compared with normal BMI, had 6% higher odds of having stunted children (AOR = 1.06; CI 1.03, 1.10; p < 0.001). Similarly, women who belong to the Scheduled Caste compared to the General Caste had 36% higher odds of having stunted children (AOR = 1.36; CI 1.30, 1.42; p < 0.001); and children aged 13–23 months compared to children up to one-year-old or younger had 141% higher odds of being stunted (AOR = 2.41; CI 2.32, 2.51; p < 0.001). The conspicuous finding is that LBW babies, after adjusting for other important confounding factors, such as BMI and ANC, experienced 19% higher odds of stunted children (AOR = 1.19; CI 1.14, 1.24; p < 0.001) compared to normal birth weight babies. Conclusions: The results revealed LBW is associated with stunting of preschool children in India.