1. An ultrasonic measurement apparatus, comprising: a measurement data acquisition unit that transmits an ultrasonic wave to a body and acquires measurement data, which is obtained by measuring a cross section of the body with the ultrasonic wave, based on a received signal; a displacement detection unit that detects displacement of a tissue in the body based on the measurement data; and a blood vessel position detection unit that detects a position of a blood vessel in the body based on the detected displacement.