We report new constraints on flavor-changing nonstandard neutrino interactions from the MINOS long-baseline experiment using νe and ¯νe appearance candidate events from predominantly νμ and ¯νμ beams. We used a statistical selection algorithm to separate νe candidates from background events, enabling an analysis of the combined MINOS neutrino and antineutrino data. We observe no deviations from standard neutrino mixing, and thus place constraints on the nonstandard interaction matter effect, |ϵeτ|, and phase, (δCP+δeτ), using a 30-bin likelihood fit