Photoacoustic microscopy (PAM) is an emerging imaging method combining light and sound. However, limited by the laser's repetition rate, state-of-the-art high-speed PAM technology often sacrifices spatial sampling density (i.e. , undersampling) for increased imaging speed over a large field-of-view. Deep learning (DL) methods have recently been used to improve sparsely sampled PAM images; however, these methods often require time-consuming pre-training and large training dataset with ground truth. Here, we propose the use of deep image prior (DIP) to improve the image quality of undersampled PAM images. Unlike other DL approaches, DIP requires neither pre-training nor fully-sampled ground truth, enabling its flexible and fast implementation on various imaging targets. Our results have demonstrated substantial improvement in PAM images with as few as 1.4 % of the fully sampled pixels on high-speed PAM. Our approach outperforms interpolation, is competitive with pre-trained supervised DL method, and is readily translated to other high-speed, undersampling imaging modalities.