This paper investigates the application of the vessel filter proposed by Frangi et al., [MICCAI, LNCS vol. 1496, pp. 130-137, 1998] to photoacoustic images of the vasculature. The filter works by classifying the eigenvalue decomposition of the local Hessian matrix at each image voxel to find tubular structures in the image. A detailed analysis of the algorithm is provided, and the effect of the filters on photoacoustic images is studied using numerical and experimental phantoms. In particular, the impact of the filter on image resolution, feature preservation, and noise is discussed. The vessel filter is then applied to photoacoustic images of the vasculature in mice. The classical Hessian filter is shown to be highly effective at removing noise and highlighting vessels, at the expense of reducing the sharpness of vessel edges.