We report new constraints on flavor-changing non-standard neutrino interactions from the MINOS long-baseline experiment using $\nu_{e}$ appearance candidate events from a predominantly $\nu_{\mu}$ beam. We used a statistical selection algorithm to separate $\nu_{e}$ 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 non-standard interaction matter effect, $\varepsilon_{e\tau}$, and phase, $(\delta_{CP}+\delta_{e\tau})$, using a thirty-bin likelihood fit.