The Tokai to Kamioka (T2K) long-baseline neutrino experiment consists of a muon neutrino beam, produced at the J-PARC accelerator, a near detector complex and a large 295-km-distant far detector. The present work utilizes the T2K event timing measurements at the near and far detectors to study neutrino time of flight as a function of derived neutrino energy. Under the assumption of a relativistic relation between energy and time of flight, constraints on the neutrino rest mass can be derived. The sub-GeV neutrino beam in conjunction with timing precision of order tens of ns provide sensitivity to neutrino mass in the few MeV/c2 range. We study the distribution of relative arrival times of muon and electron neutrino candidate events at the T2K far detector as a function of neutrino energy. The 90% C.L. upper limit on the mixture of neutrino mass eigenstates represented in the data sample is found to be m2ν<5.6  MeV2/c4.