We demonstrate that holographic particle characterization can directly detect binding of proteins to functionalized colloidal probe particles by monitoring the associated change in the particles' size. This label-free molecular binding assay uses in-line holographic video microscopy to measure the diameter and refractive index of individual probe spheres as they flow down a microfluidic channel. Pooling measurements on 104 particles yields the population-average diameter with an uncertainty smaller than 0.5 nm, which is sufficient to detect sub-monolayer coverage by bound proteins. We demonstrate this method by monitoring binding of NeutrAvidin to biotinylated spheres and binding of immunoglobulin G to spheres functionalized with protein A.