Married women have a higher risk of contracting human immunodeficiency virus (HIV) or develop acquired immune deficiency syndrome (AIDS) than men. Knowledge of HIV/AIDS contributes significantly to describing the prevalence and consequences of such virus/disease. The study aimed to investigate the level of HIV/AIDS knowledge and the socio-demographic variables that influence HIV/AIDS knowledge among married women in Bangladesh. We used three waves of Multiple Indicator Cluster Survey (MICS), which included 33,843, 20,727, and 29,724 married women from 2006, 2012, and 2019 MICS. A score was prepared through their interrogation to determine the level of knowledge and logistic regression models were used for analyzing the data. This study found that the prevalence of knowledge level of HIV/AIDS in different questions increased from 55.20% in 2006 to 58.69% in 2019. In our study, respondents having highest education had 4.03 (95% CI 3.50–4.64) times more chance to obtain “High Score” in 2019 MICS which is 5.30 times in 2012 MICS (95% CI 4.41–6.37) and 2.58 times in 2006 MICS (95% CI 2.28–2.93) compared to illiterate married women. Moreover, respondents from urban area were 1.13 times more likely to obtain “High Score” in 2019 MICS which is 1.14 times in 2012 MICS and 1.16 times in 2006 MICS, respectively than the rural married women. This study also found respondent’s age, division, mass media access, and wealth status have played an important role in HIV/AIDS knowledge. Although a significant proportion of women had adequate knowledge of HIV/AIDS, more knowledge is still required to protect against such viruses/diseases. Thus, we advocate for the implementation of educational program in the curriculum, counselling, particularly in rural areas, and mass media access to ensure quality knowledge throughout the country.