The fast blue optical transients (FBOTs) are a new population of extragalactic transients of unclear physical origin. A variety of mechanisms has been proposed including failed supernova explosion, shock interaction with a dense medium, young magnetar, accretion onto a compact object and stellar tidal disruption event, but none is conclusive. Here we report the discovery of a possible X-ray quasi-periodicity signal with a period of ∼250 s (at a significance level of 99.76%) in the brightest FBOT AT2018cow through the analysis of XMM-Newton/PN data. The signal is independently detected at the same frequency in the average power density spectrum from data taken from the Swift telescope, with observations covering from 6 to 37 days after the optical discovery, though the significance level is lower (94.26%). This suggests that the quasi-periodic oscillation (QPO) frequency may be stable over at least 1.1 × 104 cycles. Assuming the ∼250 s QPO to be a scaled-down analog of that typically seen in stellar mass black holes, a black hole mass of ∼103–105 solar masses could be inferred. The overall X-ray luminosity evolution could be modeled with a stellar tidal disruption by a black hole of ∼104 solar masses, providing a viable mechanism to produce AT2018cow. Our findings suggest that other bright FBOTs may also harbor intermediate-mass black holes.