Magnetic fluctuations in the extremely low-frequency (ELF) range from 0.1 to 10 Hz were found by the Lunar Magnetometer (LMAG) of the magnetic field and plasma experiment (MAP) on board the spacecraft Kaguya in the deepest wake behind the moon, where the magnetic field is usually quiet. The fluctuations were compressional and non-monochromatic, showing no preferred polarization. They were often accompanied by "type-II entry" solar wind protons that were reflected by the dayside lunar surface or crustal magnetic field, gyrated around the solar wind magnetic field, then entered the deepest wake. The ELF waves persisted for 30 s to several minutes. The duration was often shorter than that of the type-II protons. Most of the waves were detected on the magnetic field lines disconnected from the lunar surface, along which the solar wind electrons were injected into the wake. Since a large cross-field velocity difference is expected between the type-II protons and the solar wind electrons injected along the magnetic field, some cross-field current-driven instability such as the lower hybrid two-stream instability is expected to be responsible for the generation of the waves.