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In this paper we prequantize the moduli space of non-abelian vortices. Weexplicitly calculate the symplectic form arising from the $L^2$ metric and weconstruct a prequantum line bundle whose curvature is proportional to thissymplectic form. The prequantum line bundle turns out to be Quillen'sdeterminant line bundle with a modified Quillen metric. Next, as in the case ofabelian vortices, we construct Quillen line bundles over the moduli space whosecurvatures form a family of symplectic forms which are parametrised by$\Psi_0$, a section of a certain bundle.

Quillen bundle and geometric prequantization of non-abelian vortices on a Riemann surface