We present a monolithic integrated passively Q-switched sub-150 ps microchip laser at 1064 nm with a wedged Nd:YVO4 crystal operating up to a repetition rate of 1 MHz. The wedge enables to change the cavity length by a small amount to fine tune the spectral cavity mode position over the full gain bandwidth of Nd:YVO4 and hence to optimize the output power. This additional degree of freedom may be a suitable approach to increase the wafer scale mass production yield or also to simplify frequency tuning of CW single-frequency microchip lasers.