Example methods, apparatus, and articles of manufacture to estimate waiting times of prescriptions are disclosed herein. An example computer-implemented method, executed by a processor, to estimate a waiting time of a prescription for a medication includes training a machine learning model using, for each of a plurality of previously filled prescriptions, a set of characteristics of the previously filled prescription, and a fill time for the previously filled prescription, receiving a prescription for a medication for a patient, receiving a request for an estimated waiting time for filling the prescription medication for the patient, identifying a set of characteristics of the prescription medication for the patient, applying the set of characteristics of the prescription medication to the machine learning model to determine the estimated waiting time for filling the prescription medication for the patient, and providing an indication of the estimated waiting time for display on a client device.