Delay in vaccination schedule may result in increased risk of vaccine-preventable outbreaks. Lack of parental confidence in vaccines and sociodemographic factors could be related to those delays. Vaccine Confidence Index (VCI) is an indicator to estimate confidence in vaccines, composed of simple dimensions about it and evaluated using a 5-point Likert scale. Objectives of this study, conducted in the Region of Murcia, Spain, were to determine which sociodemographic factors were associated with delayed administration in measles, mumps and rubella (MMR) vaccine, both first and second doses, and to evaluate if there were differences in parental vaccine confidence of children who were delayed on MMR vaccine schedule compare to vaccinated on time. The 2019–2020 (first dose) and 2016–2017 (second dose) cohorts were divided into four categories: vaccinated on time, slightly delayed, moderately delayed and highly delayed. Online questionnaire was sent to their parents, followed by a telephone questionnaire for non-responders. Regarding MMR first dose, a significant association was found between delay and birth order and intellectual/motor delay of children. Parental educational status, the main source of vaccine information and the social networks more frequently used by parents were also associated with delay. Suffering motor/intellectual delay and the obstacles to vaccination process derived from caring for other siblings were associated with delay in second MMR dose. The VCI decreased significantly in first dose group as delay increases but did not change in the second one. Confidence in vaccines and sociodemographic factors, respectively, were associated with delaying MMR first and second dose.