A protease is an enzyme that catalyzes proteolysis of proteins into smaller polypeptides or single amino acids. As crucial elements in many biological processes, proteases have been shown to be informative biomarkers for several pathological conditions in humans, animals, and plants. Therefore, fast, reliable, and cost-effective protease biosensors suitable for point-of-care (POC) sensing may aid in diagnostics, treatment, and drug discovery for various diseases. This work presents an affordable and simple paper-based dipstick biosensor that utilizes peptide-encapsulated single-wall carbon nanotubes (SWCNTs) for protease detection. Upon enzymatic digestion of the peptide, a significant drop in the photoluminescence (PL) of the SWCNTs was detected. As the emitted PL is in the near-infrared region, the developed biosensor has a good signal to noise ratio in biological fluids. One of the diseases associated with abnormal protease activity is pancreatitis. In acute pancreatitis, trypsin concentration could reach up to 84 µg/mL in the urine. For proof of concept, we demonstrate the feasibility of the proposed biosensor for the detection of the abnormal levels of trypsin activity in urine samples.