We studied the hydration of a single methanol molecule in aqueous solution by first-principle DFT-based molecular dynamics simulation. The calculations show that the local structural and short-time dynamical properties of the water molecules remain almost unchanged by the presence of the methanol, confirming the observation from recent experimental structural data for dilute solutions. We also see, in accordance with this experimental work, a distinct shell of water molecules that consists of about 15 molecules. We found no evidence for a strong tangential ordering of the water molecules in the first hydration shell.