KQ Vel is a binary system composed of a slowly rotating magnetic Ap star with a companion of unknown nature. In this paper, we report the detection of its radio emission. We conducted a multi-frequency radio campaign using the ATCA interferometer (band-names: 16cm, 4cm, and 15mm). The target was detected in all bands. The most obvious explanation for the radio emission is that it originates in the magnetosphere of the Ap star, but this is shown unfeasible. The known stellar parameters of the Ap star enable us to exploit the scaling relationship for non-thermal gyro-synchrotron emission from early-type magnetic stars. This is a general relation demonstrating how radio emission from stars with centrifugal magnetospheres is supported by rotation. Using KQ Vel's parameters the predicted radio luminosity is more than five orders of magnitudes lower than the measured one. The extremely long rotation period rules out the Ap star as the source of the observed radio emission. Other possible explanations for the radio emission from KQ Vel, involving its unknown companion, have been explored. A scenario that matches the observed features (i.e. radio luminosity and spectrum, correlation to X-rays) is a hierarchical stellar system, where the possible companion of the magnetic star is a close binary (possibly of RS CVn type) with at least one magnetically active late-type star. To be compatible with the total mass of the system, the last scenario places strong constraints on the orbital inclination of the KQ Vel stellar system.