Measurements of the thermal transport properties of biological fluids and tissues are important for biomedical applications such as thermal diagnostics and thermal therapeutics. Here, we describe a microscale thermoreflectance sensor to measure the thermal effusivity of fluids and biological samples in a minimally invasive manner. The sensor is based on ultrafast optical pump-probe techniques and employs a metal-coated optical fiber as both a photonic waveguide and a local probe. Calibration of the sensor with five liquids shows that the percentage deviation between experimentally measured effusivity and literature values is on average <3%. We further demonstrate the capability of the sensor by measuring the thermal effusivity of vegetable oil, butter, pork liver, and quail egg white and yolk. We relate the thermal effusivity of the samples to their composition and water content, and establish our technique as a powerful and flexible method for studying the local thermal transport properties of biological materials.