Multiphysics urban flood models are commonly used for urban infrastructure development planning and evaluating risk due to climate change and sea level rise. However, these integrated flood models rely on several parameters that are hard to measure directly, and the resulting uncertainty in model prediction needs to be quantified, often without observable data. As a part of the Urban Flooding Open Knowledge Network (UFOKN) project, in this study we quantify parametric uncertainty in urban flood models. UFOKN incorporates flood model predictions in combination with machine learning, data and computer science, epidemiology, socioeconomics, and transportation and electrical engineering to minimize economic and human losses from future urban flooding in the United States. As a case study, we choose the Interconnected Channel and Pond Routing (ICPR) numerical model to simulate flooding in the city of Minneapolis in response to the design storms (e.g., 100-year rainfall). Through a sensitivity study, we reduce the number of uncertain model parameters to the Manning’s roughness coefficient and vertical hydraulic conductivity of soil, and construct the distributions of these parameters using open databases. We employ the multilevel Monte Carlo (MLMC) method that combines a small number of high-resolution ICPR simulations with a larger number of low-resolution simulations to reduce the computational cost of computing the key statistics of the quantities of interest describing the urban flooding. Our results show that the uncertainty in the flood predictions (as described by the coefficient of variation of the flood water depth) is distributed highly non-uniformly in the urban area with the coefficient of variation exceeding 0.5 limited to a relatively few computational elements in the ICPR model. Our results demonstrate that urban flood models such as ICPR can provide reliable flood predictions and can be used for a targeted data acquisition to further reduce the parametric uncertainty.