Institutional delivery, defined as giving birth in a health facility with skilled delivery assistants, is essential for reducing maternal mortality in low- and middle-income countries. Bangladesh has historically had high maternal mortality rates, with 452 maternal deaths per 100,000 live births in 1993, which declined to 123 per 100,000 live births in 2020. Despite this progress, the maternal mortality rate remains high, and achieving the Sustainable Development Goal (SDG) target of 70 per 100,000 live births requires further improvements in maternal healthcare, particularly in institutional delivery services. This study aimed to assess wealth-related disparities in the use of institutional delivery services in Bangladesh using data from the Multiple Indicator Cluster Survey (MICS) 2019. We applied a Wagstaff-type decomposition approach using the Erreygers-corrected concentration index (CIX) to explore wealth-related inequality in institutional delivery. Multiple logistic regression was used to identify factors associated with institutional delivery, and a CIX measured wealth-related disparities. Decomposition analysis helped identify key contributors to these disparities. Results showed that 52% of deliveries were institutional deliveries. Women from rich- and middle-income households had a 94% adjusted odds ratio (AOR = 1.94; 95% confidence intervals [CI]: 1.62–2.34) and 32% (AOR = 1.32; 95% CI: 1.12–1.56) higher likelihood, respectively, of delivering in a health institution compared to poor women. The CIX value of 0.170 indicated institutional delivery was more common among wealthier women. Decomposition analysis revealed that antenatal care (ANC) visits (33.1%), parity (11.8%), and wealth index (11.1%) were significant contributors to wealth-related disparities. In conclusion, institutional delivery remains underutilized in Bangladesh, with only half of all births occurring in health facilities. To accelerate progress in reducing maternal mortality, targeted pro-poor strategies are essential, particularly in rural and underserved areas like Mymensingh. Efforts should focus on expanding healthcare access, improving maternal education, and strengthening ANC services.