The COVID-19 pandemic has caused over 6 million deaths since 2020. To contain the spread of the virus, social distancing is one of the most simple yet effective approaches. Motivated by this, in this paper we study the problem of continuous social distance monitoring (SDM) in indoor space, in which we can monitor and predict the pairwise distances between moving objects (people) in a building in real time. SDM can also serve as the fundamental service for downstream applications, e.g., a mobile alert application that prevents its users from potential close contact with others. To facilitate the monitoring process, we propose a framework that takes the current and future uncertain locations of the objects into account, and finds the object pairs that are close to each other in a near future. We develop efficient algorithms to update the result when object locations update. We carry out experiments on both real and synthetic datasets. The results verify the efficiency and effectiveness of our proposed framework and algorithms.