A search for long-lived particles decaying to displaced, nonprompt jets and missing transverse momentum is presented. The data sample corresponds to an integrated luminosity of 137 of proton-proton collisions at a center-of-mass energy of 13 TeV collected by the CMS experiment at the CERN LHC in 2016–2018. Candidate signal events containing nonprompt jets are identified using the timing capabilities of the CMS electromagnetic calorimeter. The results of the search are consistent with the background prediction and are interpreted using a gauge-mediated supersymmetry breaking reference model with a gluino next-to-lightest supersymmetric particle. In this model, gluino masses up to 2100, 2500, and 1900 GeV are excluded at 95% confidence level for proper decay lengths of 0.3, 1, and 100 m, respectively. These are the best limits to date for such massive gluinos with proper decay lengths greater than ∼0.5 m.