The running of the top quark mass (m_t) is probed at the next-to-next-to-leading order in quantum chromodynamics for the first time. The result is obtained by comparing calculations in the modified minimal subtraction (MS) renormalisation scheme to the CMS result on differential measurement of the top quark-antiquark tt¯ production cross section at √s = 13 TeV. The scale dependence of m_t is extracted as a function of the invariant mass of the tt¯ system, up to an energy scale of about 0.5 TeV. The observed running is found to be in good agreement with the three-loop solution of the renormalisation group equations on quantum chromodynamics.