Modern genomic sequencing efforts are identifying potential diagnostic and therapeutic targets more rapidly than existing methods can generate the peptide- and protein-based ligands required to study them. To address this problem, we have developed a microfluidic enrichment device (MFED) enabling kinetic off-rate selection without the use of exogenous competitor. We tuned the conditions of the device (bed volume, flow rate, immobilized target) such that modest, readily achievable changes in flow rates favor formation or dissociation of target-ligand complexes based on affinity. Simple kinetic equations can be used to describe the behavior of ligand binding in the MFED and the kinetic rate constants observed agree with independent measurements. We demonstrate the utility of the MFED by showing a 4-fold improvement in enrichment compared to standard selection. The MFED described here provides a route to simultaneously bias pools toward high-affinity ligands while reducing the demand for target-protein to less than a nanomole per selection.