Blood flow speed is an important functional parameter. Doppler ultrasound flowmetry lacks sufficient sensitivity to slow blood flow (several to tens of millimeters per second) in deep tissue. To address this challenge, we developed ultrasonically encoded photoacoustic flowgraphy combining ultrasonic thermal tagging with photoacoustic imaging. Focused ultrasound generates a confined heat source in acoustically absorptive fluid. Thermal waves propagate with the flow and are directly visualized in pseudo color using photoacoustic computed tomography. The Doppler shift is employed to calculate the flow speed. This method requires only acoustic and optical absorption, and thus is applicable to continuous fluid. A blood flow speed as low as 0.24 mm·s-1 was successfully measured. Deep blood flow imaging was experimentally demonstrated under 5-mm-thick chicken breast tissue.