CT perfusion imaging is important in the imaging workup of acute ischemic stroke for evaluating affected cerebral tissue. CT perfusion analysis software produces cerebral perfusion maps from commonly noisy spatio-temporal CT perfusion data. High levels of noise can influence the results of CT perfusion analysis, necessitating software tuning. This work proposes a novel approach for CT perfusion analysis that uses physics-informed learning, an optimization framework that is robust to noise. In particular, we propose SPPINN: Spatio-temporal Perfusion Physics-Informed Neural Network and research spatio-temporal physics-informed learning. SPPINN learns implicit neural representations of contrast attenuation in CT perfusion scans using the spatio-temporal coordinates of the data and employs these representations to estimate a continuous representation of the cerebral perfusion parameters. We validate the approach on simulated data to quantify perfusion parameter estimation performance. Furthermore, we apply the method to in-house patient data and the public Ischemic Stroke Lesion Segmentation 2018 benchmark data to assess the correspondence between the perfusion maps and reference standard infarct core segmentations. Our method achieves accurate perfusion parameter estimates even with high noise levels and differentiates healthy tissue from infarcted tissue. Moreover, SPPINN perfusion maps accurately correspond with reference standard infarct core segmentations. Hence, we show that using spatio-temporal physics-informed learning for cerebral perfusion estimation is accurate, even in noisy CT perfusion data. The code for this work is available at https://github.com/lucasdevries/SPPINN.