The recently detected extended very-high-energy 𝛾-ray emission from the microquasar V4641 Sgr reveals a puzzling 200 parsec-long jetlike structure significantly misaligned with its radio jet. We propose that this 𝛾-ray structure is produced by high-energy cosmic-ray particles escaping from the microquasar along ordered field lines of the Galactic magnetic field and interacting with the interstellar medium. If the 𝛾-ray emission is produced by interactions of high-energy cosmic-ray nuclei, the system is detectable by future multi-km3 neutrino detectors. We argue that 𝛾-ray observations of jetlike features adjacent to high-energy sources in the Milky Way provide a new method to measure the regular and turbulent components of the Galactic magnetic field at different locations in the Milky Way.