Bangladesh is a South Asian developing country trying to achieve the Sustainable Development Goals (SDG)-3 and the objective of the Rural Electrification Board (REB) regarding child mortality. Infectious diseases are leading causes of child mortality, and lack of exclusive breastfeeding (EBF) among infants aged 0-6 months increases child morbidity and mortality from various infectious diseases in developing countries. However, as per existing literature, no study has been conducted yet to determine the lack of EBF practice effect on child mortality in Bangladesh. With this backdrop, the authors intend to measure the likelihood of infectious diseases due to the lack of EBF of infants aged 0-6 months in Bangladesh. This study used Bangladesh Demographic and Health Survey (BDHS) data over 1996-97 to 2017-18. The mothers of infants aged 0-6 months who were willingly participated in the BDHSs were considered to include in our analysis. Initially, there were 9,133 cases in the combined dataset. After filtering, there were 5,724 cases in the final dataset. We have considered diarrhea (D), acute respiratory infection (ARI) separately as well as the presence of either D or ARI or both and named as CoDARI as outcome variables. This study used both graphical and statistical techniques (Chi-square test, Wald test, and logistic regression) to analyze the data. The odds ratio (OR) and 95% confidence interval (CI) were used to quantify the likelihood of infectious diseases due to lack of EBF practice and its elasticity, respectively. The EBF practice got a conspicuous increasing trend, but the prevalence of infectious diseases was declined from 0 to 3 months of age of infants, whereas an inverse scenario is observed between 4-6 months. The significance of that inverse relationship was confirmed by p-value corresponding to the chi-square test and the Wald test of the adjusted regression coefficients after adjusting the associated factor's effect on infectious diseases. The adjusted ORs also concluded that the lack of EBF practice up to six months of age could enhance the risk of D, ARI, and CoDARI by 2.11 [95% CI: 1.56-2.85], 1.43 [95% CI: 1.28-1.60], and 1.48 [95% CI: 1.32-1.66] times higher, respectively. Findings of this study emphasize the importance of EBF up to six months of age of infants against diarrhea and ARI specific morbidity and mortality. Our results also agreed to the recommendation of the World Health Organization (WHO), United Nations International Children's Emergency Fund (UNICEF), American Academy of Pediatrics (AAP), American Academy of Family Physicians (AAFP), and National Nutrition Programme of Ethiopia (NNPE) that the EBF practice for the first six months of age could be a best, cost-effective, long-lasting natural preventive way to reduce the child morbidity and mortality due to infectious diseases in developing countries. Therefore, findings would help policymakers ensuring the achievement target of REB and SDG-3 associated with the health sector in Bangladesh.