Inspired by results of Kapranov on Atiyah classes of holomorphic vector bundles, we associate Atiyah classes to $A$-modules for any inclusion $A\into L$ of Lie algebroids. We produce a homotopy Leibniz algebra and homotopy Leibniz modules over it stemming from the Atiyah classes of the quotient $L/A$ and all other $A$-modules.