Measles remains a highly contagious and potentially severe infectious disease, necessitating high vaccine coverage. However, misinformation and measles vaccine hesitancy/resistance have posed significant challenges to achieving this goal. The COVID-19 pandemic further exacerbated these challenges, leading to a measles outbreak in Jordan in 2023. This study aimed to investigate the acceptance of the measles rubella (MR) vaccine among parents in Jordan and to identify its associated determinants. This cross-sectional questionnaire-based study was conducted using a previously Arabic-validated version of the Parental Attitudes towards Childhood Vaccines (PACV) survey instrument. Data collection took place in October 2023, and the final study sample comprised a total of 391 parents, with mothers representing 69.8% of the participants (n = 273). The majority of participating parents expressed either resistance (n = 169, 43.2%) or hesitancy (n = 168, 43.0%) towards MR vaccination, while only 54 participants (13.8%) expressed MR vaccine acceptance. Multivariate analysis revealed that trust in vaccine safety/efficacy, behavior, and having fewer offspring were significantly associated with MR vaccine acceptance. The current study revealed a concerning level of MR vaccine hesitancy/resistance among parents in Jordan, which could signal a public health alarm in the country. Urgent and targeted interventions are strongly recommended to address this issue, including mass campaigns aimed at building trust in the MR vaccine’s safety/efficacy. Additionally, there is an urgent need for effective public health initiatives to ensure sufficient measles vaccine coverage to prevent future outbreaks of this serious disease.