Background In many low- and middle-income countries (LMICs), including Bangladesh, socioeconomic inequalities in access to maternity care remain a substantial public health concern. Due to the paucity of research, we attempted to determine the factors affecting the facility delivery, quantify wealth-related inequality, and identify potential components that could explain the inequality. Methods We used the latest Bangladesh Demographic and Health Survey (BDHS 2017–18) data in this study. We utilized logistic regression to investigate the associated factors of facility delivery. The concentration curves (CC), concentration index (CIX) and decomposition of CIX techniques were used to analyze the inequality in-facility delivery. Results Women living in the urban areas, age at first birth after (18–24 years ≥25 years), being overweight/obese, having secondary and higher-level education of the women and their husband, seeking four or more ANC, coming from more affluent households, and women with high enlightenment were significant determinants of facility delivery. The concentration curve was below the line of equality, and the relative concentration index (CIX) was 0.205 (p <0.001), indicating that women from wealthy groups were disproportionately more prevalent to facility delivery. The decomposition analysis reveals that wealth status of women (57.40%), age at first birth (10.24%), husband’s education (8.96%), husband’s occupation (7.35%), education of women (7.13%), women’s enlightenment (6.15%), residence (8.64%) and ANC visit (6.84%) are the most major contributors to the inequalities in utilizing facility delivery. Conclusion The study demonstrates a clear disparity in the use of facility delivery among Bangladeshi women; hence, immediate action is required to lower the inequalities, with a special emphasis on the contributing factors.