Urine is an attractive biospecimen for in vitro diagnostics, and urine-based lateral flow assays are low-cost devices suitable for point-of-care testing, particularly in low-resource settings. However, some of the lateral flow assays exhibit limited diagnostic utility because the urinary biomarker concentration is significantly lower than the assay detection limit, which compromises the sensitivity. To address the challenge, we developed an osmotic processor that statically and spontaneously concentrated biomarkers. The specimen in the device interfaces with the aqueous polymer solution via a dialysis membrane. The polymer solution induces an osmotic pressure difference that extracts water from the specimen, while the membrane retains the biomarkers. The evaluation demonstrated that osmosis induced by various water-soluble polymers efficiently extracted water from the specimens, ca. 5–15 ml/h. The osmotic processor concentrated the specimens to improve the lateral flow assays’ detection limits for the model analytes—human chorionic gonadotropin and SARS-CoV-2 nucleocapsid protein. After the treatment via the osmotic processor, the lateral flow assays detected the corresponding biomarkers in the concentrated specimens. The test band intensities of the assays with the concentrated specimens were very similar to the reference assays with 100-fold concentrations. The mass spectrometry analysis estimated the SARS-CoV-2 nucleocapsid protein concentration increased ca. 200-fold after the osmosis. With its simplicity and flexibility, this device demonstrates a great potential to be utilized in conjunction with the existing lateral flow assays for enabling highly sensitive detection of dilute target analytes in urine.