This paper presents a phase-based method for estimating subpixel motion in medical ultrasound imaging. The main novelty is to propose a closed form expression for local motion estimation in space domain based on the model of the monogenic signal. First, the proposed method uses the properties of the monogenic signal in order to extract local orientation and phase data of ultrasound images. Second, using these image features, we show how the proposed method can analytically estimate the dense motion field between a pair of images. This way of estimating motion provides subpixel accuracy without interpolating the images. For this reason, we show that the proposed method has high computational efficiency. Results on simulated and experimental data show that this method provides a better Contrast to Noise Ratio than a classical block-matching method applied to images that are 25 times larger (in number of pixels).