We report the first observation of seasonal modulations in the rates of cosmic ray multiple-muon events at two underground sites, the MINOS Near Detector with an overburden of 225 mwe, and the MINOS Far Detector site at 2100 mwe. At the deeper site, multiple-muon events with muons separated by more than 8 m exhibit a seasonal rate that peaks during the summer, similar to that of single-muon events. In contrast and unexpectedly, the rate of multiple-muon events with muons separated by less than 5-8 m, and the rate of multiple-muon events in the smaller, shallower Near Detector, exhibit a seasonal rate modulation that peaks in the winter.