Context. Astrophysical observations show complex organic molecules (COMs) in the gas phase of protoplanetary disks. X-rays emitted from the central young stellar object that irradiate interstellar ices in the disk, followed by the ejection of molecules in the gas phase, are a possible route to explain the abundances observed in the cold regions. This process, known as X-ray photodesorption, needs to be quantified for methanol-containing ices. This Paper I focuses on the case of X-ray photodesorption from pure methanol ices. Aims. We aim at experimentally measuring X-ray photodesorption yields (in molecule desorbed per incident photon, displayed as molecule/photon for more simplicity) of methanol and its photo-products from pure CH 3 OH ices, and to shed light on the mechanisms responsible for the desorption process. Methods. We irradiated methanol ices at 15 K with X-rays in the 525-570 eV range from the SEXTANTS beam line of the SOLEIL synchrotron facility. The release of species in the gas phase was monitored by quadrupole mass spectrometry, and photodesorption yields were derived. Results. Under our experimental conditions, the CH 3 OH X-ray photodesorption yield from pure methanol ice is ∼10 −2 molecule/photon at 564 eV. Photo-products such as CH 4 , H 2 CO, H 2 O, CO 2 , and CO also desorb at increasing efficiency. X-ray photodesorption of larger COMs, which can be attributed to either ethanol, dimethyl ether, and/or formic acid, is also detected. The physical mechanisms at play are discussed and must likely involve the thermalization of Auger electrons in the ice, thus indicating that its composition plays an important role. Finally, we provide desorption yields applicable to protoplanetary disk environments for astrochemical models. Conclusions. The X-rays are shown to be a potential candidate to explain gas-phase abundances of methanol in disks. However, more relevant desorption yields derived from experiments on mixed ices are mandatory to properly support the role played by X-rays in nonthermal desorption of methanol (see Paper II).