Conventional manufacturing of microfluidic devices from glass substrates is a complex, multi-step process that involves different fabrication techniques and tools. Hence, it is time-consuming and expensive, in particular for the prototyping of microfluidic devices in low quantities. This article describes a laser-based process that enables the rapid manufacturing of enclosed micro-structures by laser micromachining and microwelding of two 1.1-mm-thick borosilicate glass plates. The fabrication process was carried out only with a picosecond laser (Trumpf TruMicro 5×50) that was used for: (a) the generation of microfluidic patterns on glass, (b) the drilling of inlet/outlet ports into the material, and (c) the bonding of two glass plates together in order to enclose the laser-generated microstructures. Using this manufacturing approach, a fully-functional microfluidic device can be fabricated in less than two hours. Initial fluid flow experiments proved that the laser-generated microstructures are completely sealed; thus, they show a potential use in many industrial and scientific areas. This includes geological and petroleum engineering research, where such microfluidic devices can be used to investigate single-phase and multi-phase flow of various fluids (such as brine, oil, and CO2) in porous media.