The continental crust is strongly depleted in copper compared with its building blocks-primary arc magmas-and this depletion is intrinsically associated with continental crust formation. However, the process by which Cu removal occurs remains enigmatic. Here we show, using Cu isotopes, that subduction-zone processes and mantle melting produce limited fractionation of Cu isotopes in arc magmas, and, instead, the heterogeneous Cu isotopic compositions of lower crustal rocks, which negatively correlate with Cu contents, suggest segregation or accumulation of isotopically light sulfides during intracrustal differentiation of arc magmas. This is supported by the extremely light Cu isotopic compositions of lower crustal mafic cumulates and heavy Cu isotopic compositions of differentiated magmas in thick continental arcs. Intracrustal differentiation of mantle-derived magmas and subsequent foundering of sulfide-rich mafic cumulates preferentially removes isotopically light Cu, leaving a Cu-depleted and isotopically heavy continental crust.