The nuclear envelope is a membrane separating nuclear from cytoplasmic processes. Existing models suggest that damaged DNA moves to the envelope at the edge of the nucleus for repair. Yet, most damaged human DNA does not reposition to the nuclear periphery during repair. Here we show that human cells relocate the nuclear envelope to non-peripheral damaged DNA, providing solid support promoting the reconnection of DNA break ends. Upon DNA double-strand break (DSB) induction, cytoplasmic microtubules poke the nuclear envelope inwards, inducing an extensive network of DSB-capturing nuclear envelope tubules (dsbNETs). The formation of dsbNETs, which encompass the nuclear lamina and the inner and outer nuclear membranes, depends on DNA damage response kinases, dynamic microtubules, the linker of the nucleoskeleton and cytoskeleton (LINC) proteins SUN1 and SUN2, nuclear pore protein NUP153, and kinesin KIF5B. Repressing dsbNETs compromises the reassociation of DSB ends. The timely reversal of dsbNETs by the kinesin KIFC3 also promotes repair. DSB ends reconnection is restored in dsbNETs-deficient cells by enlarging the 53BP1 DNA repair center. The lamina-binding domain of SUN1 mediates its entry into the tubules and DSB capture by the envelope. Fusing truncated SUN1 to the NHEJ repair protein KU70 fails to localize SUN1 to the tubules but rescues DSB targeting only to the boundary envelope. Although dsbNETs typically promote accurate DSB repair and cell survival, they are co-opted by the PARP inhibitor olaparib to induce aberrant chromosomes restraining BRCA1-deficient breast cancer cells. We uncover dsbNETs, which bring the nuclear envelope to DSBs for repair and potentiate the efficacy of anti-cancer agents. Our findings revise theories of the structure-function relationship of the nuclear envelope and identify dsbNETs as a critical factor in DNA repair and nuclear organization, with implications for health and disease.