A Weyl semimetal with broken time-reversal symmetry has a minimum of two species of Weyl fermions, distinguished by their opposite chirality, in a pair of Weyl cones at opposite momenta ±K that are displaced in the direction of the magnetization. Andreev reflection at the interface between a Weyl semimetal in the normal state (N) and a superconductor (S) that pairs ±K must involve a switch of chirality, otherwise it is blocked. We show that this "chirality blockade" suppresses the superconducting proximity effect when the magnetization lies in the plane of the NS interface. A Zeeman field at the interface can provide the necessary chirality switch and activate Andreev reflection.