Constraints are presented on the total width of the recently discovered Higgs boson, (\Gamma_H), using its relative on-shell and off-shell production and decay rates to a pair of Z bosons, where one Z boson decays to an electron or muon pair, and the other to an electron, muon, or neutrino pair. The analysis is based on the data collected by the CMS experiment at the LHC in 2011 and 2012, corresponding to integrated luminosities of 5.1 fb⁻¹ at a center-of-mass energy (\sqrt{s}) = 7 TeV and 19.7 fb⁻¹ at (\sqrt{s}) = 8 TeV. A simultaneous maximum likelihood fit to the measured kinematic distributions near the resonance peak and above the Z-boson pair production threshold leads to an upper limit on the Higgs boson width of (\Gamma_H) < 22 MeV at a 95% confidence level, which is 5.4 times the expected value in the standard model at the measured mass of (m_H) = 125.6 GeV.