Interactions of cosmic rays with the Moon and the Sun produce deficits in their arrival-direction distributions relative to an isotropic flux. Such shadows have been observed previously at energies between ${10}^{12}$eV and ${10}^{16}$eV. We report the first evidence for the Moon and Sun shadows at cosmic-ray energies larger than about ${10}^{16}$eV (average energy of $7\times {10}^{17}$eV), using data collected by the Pierre Auger Observatory. We employ data from three detector arrays covering $3000{\mathrm{\text{km}}}^2$, $27{\mathrm{\text{km}}}^2$, and $2{\mathrm{\text{km}}}^2$, with spacings of $1500\mathrm{\text{m}}$, $750\mathrm{\text{m}}$, and $433\mathrm{\text{m}}$, respectively. The data amount to over 10.6 million events. The Moon and Sun shadows are detected with a combined significance of approximately $3\sigma$. These observations confirm the pointing accuracy of the Surface Detector of the Pierre Auger Observatory using celestial bodies. From the combined Sun and Moon shadows, we infer an overall angular resolution of $({0.59}_{-0.11}^{+0.15}{)}^{\circ }$.