We report observations of the exoplanet host-star HD 80606 using the OSIRIS tunable filter imager. Very-high-precision, narrow-band photometry in four bandpasses around the K I absorption feature was acquired during the January 2010 transit of HD 80606b, with further off-transit observations taken January and April of 2010. We obtained differential photometric precisions of ~2.08×10^-4 for the in-transit flux ratio measured at 769.91 nm, which probes the K I line core. The observed changes in the depth of the transit across several wavelengths is equivalent to a ~4.2% change in the apparent planetary radius with wavelength, which is much larger than the atmospheric scale height. This implies the observations probed the atmosphere at very low pressures as well as a dramatic change in the pressure at which the optical depth reaches unity across the bands observed. We hypothesize that the excess absorption may be due to K I in a high-speed wind being driven from the exoplanet's exosphere and discuss the viability of this and alternative interpretations. We also present similar observations of the exoplanet XO-2b that were acquired recently and which are currently being analysed. Finally, we discuss future prospects for exoplanet characterization using tunable filter spectrophotometry.