The existence of a lunar Mach cone in the flow of the magnetized warm collisionless solar plasma has been determined from magnetometer data on lunar Explorer 35. The axis of the Mach cone indicates that the direction of the solar wind comes from ∼4.5° west of the sun as viewed from the moon. Owing to the variability of the magnetic field direction, the spacecraft has actually observed the three-dimensional wake region of the interaction of the solar wind with the moon. The lack of axial symmetry of the observed lunar Mach cone provides the first experimental evidence for the anisotropic propagation of magnetoacoustic waves in the solar wind. The average Mach angle is found to be ∼8° in directions perpendicular to the magnetic field vector and ∼5.5° in the direction parallel to the field; this leads to a velocity anisotropy of V⊥/V∥ = 1.4. This value compares favorably with the nominal expected value in the solar wind of ∼1.5, if β = 1 and T∥/T⊥ = 1.2.