We experimentally investigate the role of sample size on the viscosity of a bulk metallic glass by examining pressure driven flows in nm-scale confinement. A Pt57.5Cu14.7Ni5.3P22.5 metallic glass in the super-cooled liquid state is extruded into isolated cylindrical pores of varying nano-scale dimensions, down to 40 nm. The apparent viscosity of the liquid as a function of sample size is determined from the filling depth by appropriate corrections to the Hagen-Poiseuille equation. We observe a striking, sudden increase of the apparent viscosity for dimensions below approximately 100 nm. Results are discussed in the framework of confinement of collective shear events.