The antiferromagnetic structure of Yb_{3}Ga_{5}O_{12} is identified by neutron diffraction experiments below the previously known transition at T_{λ}=54 mK. The magnetic propagation vector is found to be k=(1/2,1/2,0), an unusual wave vector in the garnet structure. The associated complex magnetic structure highlights the role of exchange interactions in a nearly isotropic system dominated by dipolar interactions and finds echoes with exotic structures theoretically proposed. Reduced values of the ordered moments may indicate significant quantum fluctuations in this effective spin-1/2 geometrically frustrated magnet.