Estimation of water and contaminant discharges is an important hydrological problem. Fractured rock aquifers are recognized as highly complex flow and transport systems, and the fractured rock passive flux meter (FRPFM) is a recently tested device to simultaneously measure cumulative water and contaminant mass fluxes in fractures intersecting an observation well (boring). Furthermore, the FRPFM is capable of indicating orientations and directions of flow in hydraulically active (“flowing”) fractures. The present work develops a discharge estimator for when FRPFM measurements of fracture fluxes in the direction perpendicular to a transect (control plane) along one or more observation wells are available. In addition, estimation uncertainty in terms of a coefficient of variation is assessed based on a Monte Carlo approach under normalized conditions. Sources of uncertainty considered are spatially random fracture trace locations, random trace lengths, and orientations as well as variability of trace average fluxes (including smooth spatial trends), variability of local fluxes within traces, and flux measurement errors. Knowledge about the trace length distribution, which is commonly not available from borehole surveys, is not required for discharge estimation. However, it does affect the uncertainty assessment, and equations for upper uncertainty bounds are given as an alternative. In agreement with general statistical inference, it is found that discharge uncertainty decreases proportionally with the number of fluxes measured. Results are validated, and an example problem illustrates practical application and performance.