We report the first observation of the spontaneous polarization of $Lambda$ and $bar{Lambda}$ hyperons transverse to the production plane in $e^+e^-$ annihilation, which is attributed to the effect arising from a polarizing fragmentation function. For inclusive $Lambda/bar{Lambda}$ production, we also report results with subtracted feed-down contributions from $Sigma^0$ and charm. This measurement uses a dataset of 800.4 fb$^{-1}$ collected by the Belle experiment at or near a center-of-mass energy of 10.58 GeV. We observe a significant polarization that rises with the fractional energy carried by the $Lambda/bar{Lambda}$ hyperon.