We report the first observation of the spontaneous polarization of Λ and Λ[over ¯] hyperons transverse to the production plane in e^{+}e^{-} annihilation, which is attributed to the effect arising from a polarizing fragmentation function. For inclusive Λ/Λ[over ¯] production, we also report results with subtracted feed-down contributions from Σ^{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 Λ/Λ[over ¯] hyperon.