The first measurements of skewness and kurtosis of mean transverse momentum (⟨𝑝T⟩) fluctuations are reported in Pb–Pb collisions at √𝑠NN = 5.02 TeV, Xe–Xe collisions at √𝑠NN = 5.44 TeV and pp collisions at √𝑠 = 5.02 TeV using the ALICE detector. The measurements are carried out as a function of system size ⟨d𝑁ch∕d𝜂⟩ 1∕3 |𝜂|< 𝑝T < 3.0 GeV/c and |𝜂| < 0.8, respectively. In Pb–Pb and Xe–Xe collisions, positive skewness is observed in the fluctuations of ⟨𝑝T⟩ for all centralities, which is significantly larger than what would be expected in the scenario of independent particle emission. This positive skewness is considered a crucial consequence of the hydrodynamic evolution of the hot and dense nuclear matter created in heavy-ion collisions. Furthermore, similar observations of positive skewness for minimum bias pp collisions are also reported here. Kurtosis of ⟨𝑝T⟩ fluctuations is found to be in good agreement with the kurtosis of Gaussian distribution, for most central Pb–Pb collisions. Hydrodynamic model calculations with MUSIC using Monte Carlo Glauber initial conditions are able to explain the measurements of both skewness and kurtosis qualitatively from semicentral to central collisions in Pb–Pb system. Color reconnection mechanism in PYTHIA8 model seems to play a pivotal role in capturing the qualitative behavior of the same measurements in pp collisions.