Monitoring the kinetics of protein interactions on a high-density sensor array is vital to drug development and proteomic analysis. Label-free kinetic assays based on surface plasmon resonance are the current gold standard, but they have poor detection limits, suffer from non-specific binding, and are not amenable to high-throughput analyses. Here, we show that magnetically responsive nanosensors that have been scaled to over 100,000 sensors per cm² can be used to measure the binding kinetics of various proteins with high spatial and temporal resolution. We present an analytical model that describes the binding of magnetically labelled antibodies to proteins that are immobilized on the sensor surface. This model is able to quantify the kinetics of antibody-antigen binding at sensitivities as low as 20 zeptomoles of solute.