The authors show that the operator norm of every Banach space valued Calderón-Zygmund operator \(T\) on the weighted Lebesgue-Bochner space depends linearly on the Muckenhoupt \(A_2\) characteristic of the weight. In parallel with the proof of the real-valued case, the proof is based on pointwise dominating every Banach space valued Calderón-Zygmund operator by a series of positive dyadic shifts. In common with the real-valued case, the pointwise dyadic domination relies on Lerner’s local oscillation decomposition formula, which the authors extend from the real-valued case to the Banach space valued case. This extension is based on a Banach space valued generalization of the notion of median.