We developed a molecular sorter that operates without external power or control by integrating the microtubule-based, biological motor kinesin into a microfluidic channel network to sort, transport, and concentrate molecules. In our devices, functionalized microtubules that capture analyte molecules are steered along kinesin-coated microchannel tracks toward a collector structure, concentrated, and trapped. Using fluorescent analyte molecules and nanoliter sample volumes, we demonstrated 14 fM sensitivity, even in the presence of high concentrations of other proteins.