A vehicle wheel assembly position measurement apparatus measures, at each of at least three measurement positions in a circumferential direction, a distance in a vehicle width direction between each of plural measurement points located on a specified line that crosses a lateral surface of a tire section from an inner circumferential end to an outer circumferential end and a respective one of distance measuring instruments, calculates an approximate curve indicating a relationship between a position in an extending direction of the specified line and the distance of each of the measurement points at the respective measurement position, calculates a rotation center position of a wheel assembly from a specific position of the approximate curve at the measurement position, and calculates a height position of the wheel assembly relative to a vehicle body from the rotation center position and a height position of a specified portion of the vehicle body.