The prevalence of stunting among children below 5 years of age is higher in the slum-dwelling population of Bangladesh compared to that in both urban and rural areas. Studies have reported that several factors such as inadequate nutrition, low socio-economic status, poor hygiene and sanitation and lack of maternal education are the substantial predictors of childhood stunting. Almost all these factors are universally present in the slum-dwelling population of Bangladesh. However, few studies have prospectively examined such determinants of stunting among slum populations. In this paper, we reveal the findings of a cohort study with an aim to explore the status of micronutrient adequacy among such vulnerable children and establish its association with stunting along with other determinants. Two-hundred-sixty-five children were enrolled and followed since birth until 24 months of age. We collected anthropometric, morbidity and dietary intake data monthly. We used the 24-hour multiple-pass recall approach to collect dietary intake data from the age of 9 months onward. Micronutrient adequacy of the diet was determined by the mean adequacy ratio (MAR) which was constructed from the average intake of 9 vitamins and 4 minerals considered for the analysis. We used generalized estimating equation (GEE) regression models to establish the determinants of stunting between 12–24 months of age in our study population. The prevalence of low-birth-weight (LBW) was about 28.7% and approximately half of the children were stunted by the age of 24 months. The average micronutrient intake was considerably lower than the recommended dietary allowance and the MAR was only 0.48 at 24 months of age compared to the optimum value of 1. However, the MAR was not associated with stunting between 12–24 months of age. Rather, LBW was the significant determinant (AOR = 3.03, 95% CI: 1.69–5.44) after adjusting for other factors such as age (AOR = 2.12, 95% CI: 1.45–3.11 at 24 months and AOR = 1.97, 95% CI: 1.49–2.59 at 18 months, ref: 12 months) and sex (AOR = 1.98, 95% CI: 1.17–3.33, ref: female). Improving the nutritional quality of complementary food in terms of adequacy of micronutrients is imperative for optimum growth but may not be adequate to mitigate under-nutrition in this setting. Further research should focus on identifying multiple strategies that can work synergistically to diminish the burden of stunting in resource-poor settings.