Since the discovery of the photovoltaic properties of metal halide perovskites in 2009, the material has rapidly gained interest in the scientific community. In less than 10 years, the power conversion efficiency of perovskite solar cells (PSC) has increased from 3.9% to over 25%, reaching levels of conventional silicon cells. PSCs have multiple favorable properties, such as low manufacturing costs, thin film flexibility, and a tunable bandgap, which is promising for tandem solar cells that can surpass the Shockley-Queisser efficiency limit of conventional (single-junction) solar cells. Other applications are color-tunable LEDs and super sensitive (x-ray) photodetectors. However, there are still mysteries surrounding perovskites that need to be solved in order to fully understand the extraordinary properties of the material. For a specific perovskite, CH3NH3PbI3 (MAPI), it is debated whether it has a direct or indirect bandgap. In this work, a new Photothermal Deflection Spectroscopy (PDS) setup is designed and build that can perform sensitive below-bandgap absorption measurements under hydrostatic pressure (up to 400 MPa). Measurements performed with this setup resulted in absorption spectra of MAPI at different pressures, showing a transition from a primarily indirect bandgap at ambient pressure to a more direct bandgap at 375MPa. The data provides new empirical evidence indicating an indirect-to-direct bandgap transition at 325MPa, which opens a novel perspective on unraveling the nature of the bandgap of metal halide perovskites.