The ϵ Lupi A (HD 136504) system stands out among magnetic massive binaries as the only short-period binary system in which both components have detectable magnetic fields. The proximity of the magnetospheres of the components leads to magnetospheric interactions, which are revealed as periodic pulses in the radio light curve of this system. In this work, we aim to investigate the magnetospheric interaction phenomenon in the X-ray domain. We observed this system with the XMM-Newton telescope, covering its orbital period. We observe variable X-ray emission with maximum flux near periastron, showing similarity with radio observations. The X-ray spectra show significantly elevated hard X-ray flux during periastron. We attribute the soft X-ray emission to individual magnetospheres, while the hard X-ray emission is explained by magnetospheric interaction, particularly due to magnetic reconnection. However, unlike in the radio, we do not find any significant short-term X-ray bursts. This exotic system may be an ideal target to study magnetospheric interactions in close binaries with organized magnetospheres.