We present fluorescence recovery measurements after photobleaching performed under high pressure in liquids that fill square-section fused silica micro-capillaries. These micro-capillaries withstand pressure up to 2500 bar for a wall thickness of about 140 μm and fit easily on the microscope stage. This technique allows the translational diffusion coefficient of fluorescent molecules in liquids to be measured as a function of pressure. When the liquid sample is far from its glass transition the translational diffusive coefficient is in agreement with the Stokes-Einstein equation. As the glass transition is approached by further increasing the pressure, decoupling of the measured diffusion coefficient from the Stokes-Einstein relation is observed. These are the first measurements that combine the fluorescence recovery technique and high hydrostatic pressures. This experimental setup can also be used either with diamond or sapphire anvil cells in order to span a larger pressure range.