Systems, methods, and instructions encoded in a computer-readable medium can perform operations related to generating probabilistic information on characteristics of natural fractures of a subterranean formation. Fitted fracture models are generated based on microseismic event data for a subterranean region. The fitted fracture models represent estimated locations of fractures in the subterranean region. A distribution of fracture parameter values is generated based on the fitted fracture models. The distribution includes fracture parameter values and a probability associated with each fracture parameter value. Generating the fitted fracture models may include, for example, fitting a plane, a line or another type of equation to the measured locations of microseismic events. In some implementations, an injection treatment may be simulated and/or designed based on the probability distribution.