We present a 50 μm Nd3+:YVO4 microchip laser that is passively Q-switched by a semiconductor saturable absorber mirror. To reduce handling problems caused by the small crystal dimensions, the 50 μm Nd3+:YVO4 crystal is optically bonded to an undoped YVO4 crystal of a length of about 500 μm. By using a saturable absorber mirror with an effective modulation depth of >10% the system is able to deliver 16 ps pulses at a repetition rate of up to 1.0 MHz. The average laser power is 16 mW at 1064 nm. To our knowledge these are the shortest Q-switched pulses ever reported from a solid-state laser. The limits in terms of pulse width, repetition rate, output power, and system stability are discussed. Additionally, continuous-wave behavior is analyzed. Experimental data is compared with the simulation results of the coupled rate equations.