Disjoint interval-censored (DIC) observations are found in a variety of applications including survey responses, contingent valuation studies and grouped data. Despite being a recurrent type of data, little attention has been given to their analysis in the nonparametric literature. In this study, we develop an alternative approach for the estimation of the empirical distribution function of DIC data by optimizing their nonparametric maximum likelihood (ML) function. In contrast to Turnbull’s standard nonparametric method, our estimation approach does not require iterative numerical algorithms or the use of advanced statistical software packages. In fact, we demonstrate the existence of a simple closed-form solution to the nonparametric ML problem, where the empirical distribution, its variance, and measures of central tendency can be estimated by using only the frequency distribution of observations. The advantages of our estimation approach are illustrated using two empirical datasets.