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We use a sample of 87 rest-frame UV-selected star-forming galaxies with mean spectroscopic redshift z=2.26 to study the correlation between metallicity and stellar mass at high redshift. Using stellar masses determined from SED fitting to 0.3-8 micron photometry, we divide the sample into six bins in stellar mass, and construct six composite H-alpha+[NII] spectra from all of the objects in each bin. We estimate the mean oxygen abundance in each bin from the [NII]/H-alpha ratio, and find a monotonic increase in metallicity with increasing stellar mass, from 12+log(O/H) < 8.2 for galaxies with <M_star> = 2.7e9 Msun to 12+log(O/H) = 8.6 for galaxies with <M_star> = 1e11 Msun. We use the empirical relation between star formation rate density and gas density to estimate the gas fractions of the galaxies, finding an increase in gas fraction with decreasing stellar mass. These gas fractions combined with the observed metallicities allow the estimation of the effective yield y_eff as a function of stellar mass; in constrast to observations in the local universe which show a decrease in y_eff with decreasing baryonic mass, we find a slight increase. Such a variation of metallicity with gas fraction is best fit by a model with supersolar yield and an outflow rate ~4 times higher than the star formation rate. We conclude that the mass-metallicity relation at high redshift is driven by the increase in metallicity as the gas fraction decreases through star formation, and is likely modulated by metal loss from strong outflows in galaxies of all masses. There is no evidence for preferential loss of metals from low mass galaxies as has been suggested in the local universe. [Abridged]