Infinitesimal derived foliations provide a derived analogue of algebraic foliations in arbitrary characteristics. We use the method of PD Koszul duality to relate infinitesimal derived foliations with partition Lie algebroids, and answer positively a conjecture of Toën and Vezzosi. The comparison theorem implies some formal integrability properties of infinitesimal derived foliations, which might be helpful for the algebraization problem of singular algebraic foliations.