An ultrasensitive lateral-flow assay is developed for rapid quantitative detection of small molecules on-site. The conceptual novelty, which transfers lateral-flow assays to the category of highly sensitive quantitative systems, is due to employment of a bifunctional ligand combined with volumetric registration of magnetic nanolabels. The ligand provides extremely high affinity for trapping the nanolabels and, simultaneously, efficiently competes with the analyzed molecules for the limited quantity of antigen-binding sites on the nanolabels. The developed assay has been demonstrated as the first express method for measuring in human serum of free thyroxine (fT4). The limit of detection is 20 fМ or 16 fg/ml at the assay time <30 min with the dynamic range of 3 orders. Besides, we present the results of first characterization of kinetic parameters of interaction between free thyroxine and monoclonal antibody, as well as of competitive relationship between fT4 and fT4-biotin. The proposed universal platform can be used for ultrasensitive detection of small molecules in human in vitro diagnostics, veterinary, biosafety and counter-terrorism, food quality control, environmental monitoring, etc., as well as for search of new, previously undetectable, diagnostic markers in medicine.