Classification of human movements is an important problem in healthcare and well-being applications. An ultrasonic array Doppler sensing method is proposed for classifying movements from a given set. The proposed method uses velocity and angular information derived from Doppler frequencies and direction-of-arrival (DoA) by processing the signals at the receiver sensor array. Doppler frequency estimation is done by obtaining an initial estimate based on the Fourier transform in conjunction with a predictive tracker. A Root-MUSIC algorithm is used at the estimated Doppler frequencies to obtain DoA corresponding to the dominating moving object. Using speed, direction, and angle as features, a Bayesian classifier is employed to distinguish between a set of movements. The performance of the proposed method is evaluated using an analytical model of arm movements and also using experimental data sets. The proposed ultrasonic Doppler array sensor and processing methods provide a new, compact solution to human arm movement classification.