The MoEDAL trapping detector consists of approximately 800 kg of aluminum volumes. It was exposed during run 2 of the LHC program to 6.46 fb^{-1} of 13 TeV proton-proton collisions at the LHCb interaction point. Evidence for dyons (particles with electric and magnetic charge) captured in the trapping detector was sought by passing the aluminum volumes comprising the detector through a superconducting quantum interference device (SQUID) magnetometer. The presence of a trapped dyon would be signaled by a persistent current induced in the SQUID magnetometer. On the basis of a Drell-Yan production model, we exclude dyons with a magnetic charge ranging up to five Dirac charges (5g_{D}) and an electric charge up to 200 times the fundamental electric charge for mass limits in the range 870-3120 GeV and also monopoles with magnetic charge up to and including 5g_{D} with mass limits in the range 870-2040 GeV.