Abstract γ-ray observations of the Cygnus Cocoon, an extended source surrounding the Cygnus X star-forming region, suggest the presence of a cosmic-ray accelerator reaching energies up to a few PeV. The very-high-energy (VHE; 0.1–100 TeV) γ-ray emission may be explained by the interaction of cosmic-ray hadrons with matter inside the Cocoon, but an origin of inverse Compton radiation by relativistic electrons cannot be ruled out. Inverse Compton γ-rays at VHE are accompanied by synchrotron radiation peaked in X-rays. Hence, X-ray observations may probe the electron population and magnetic field of the source. We observed 11 fields in or near the Cygnus Cocoon with the Neil Gehrels Swift Observatory’s X-Ray Telescope (Swift-XRT) totaling 110 ks. We fit the fields to a Galactic and extragalactic background model and performed a log-likelihood ratio test for an additional diffuse component. We found no significant additional emission and established upper limits in each field. By assuming that the X-ray intensity traces the TeV intensity and follows a dN / dE ∝ E − 2.5 spectrum, we obtained a 90% upper limit of F _X < 8.7 × 10⁻¹¹ erg cm⁻² s⁻¹ or <5.2 × 10⁻¹¹ erg cm⁻² s⁻¹ on the X-ray flux of the entire Cygnus Cocoon between 2 and 10 keV depending on the choice of hydrogen column density model for the absorption. The obtained upper limits suggest that no more than one-quarter of the γ-ray flux at 1 TeV is produced by inverse Compton scattering, when assuming an equipartition magnetic field of ∼20 μG.