An acoustic wave measurement apparatus includes: an image display unit that displays an acoustic wave image; a measurement target designation receiving unit that receives designation of a measurement target; a position designation receiving unit that receives designation of a position of a measurement target on the acoustic wave image displayed on the image display unit; a measurement method information receiving unit that receives measurement method information indicating a measurement method; a detection measurement algorithm setting unit that sets a detection measurement algorithm based on the measurement target received by the measurement target designation receiving unit and the measurement method information received by the measurement method information receiving unit; and a measurement unit that detects the measurement target based on the received position and the detection measurement algorithm and performs measurement for the detected measurement target.