Although genetic and epigenetic abnormalities in breast cancer have been extensively studied, it remains difficult to identify those patients who will respond to particular therapies. This is due in part to our lack of understanding of how the variability of cellular signaling affects drug sensitivity. Here, we used mass cytometry to characterize the single-cell signaling landscapes of 62 breast cancer cell lines and five lines from healthy tissue. We quantified 34 markers in each cell line upon stimulation by the growth factor EGF in the presence or absence of five kinase inhibitors. These data – on more than 80 million single cells from 4,000 conditions – were used to fit mechanistic signaling network models that provide unprecedented insights into the biological principles of how cancer cells process information. Our dynamic single-cell-based models more accurately predicted drug sensitivity than static bulk measurements for drugs targeting the PI3K-MTOR signaling pathway. Finally, we identified genomic features associated with drug sensitivity by using signaling phenotypes as proxies, including a missense mutation in DDIT3 predictive of PI3K-inhibition sensitivity. This provides proof of principle that single-cell measurements and modeling could inform matching of patients with appropriate treatments in the future.