We present an all-sky 90% confidence level upper limit on the cosmic flux of relativistic magnetic monopoles using 2886 days of IceCube data. The analysis was optimized for monopole speeds between 0.750 c and 0.995 c , without any explicit restriction on the monopole mass. We constrain the flux of relativistic cosmic magnetic monopoles to a level below 2.0×10−19 cm−2 s−1 sr−1 over the majority of the targeted speed range. This result constitutes the most strict upper limit to date for magnetic monopoles with β ≳0.8 and up to β ∼0.995 and fills the gap between existing limits on the cosmic flux of nonrelativistic and ultrarelativistic magnetic monopoles.