Targeting protein degradation with Proteolysis-Targeting Chimeras (PROTACs) is an area of great current interest in drug discovery. Nevertheless, although the high effectiveness of PROTACs against a wide variety of targets has been established, most degraders reported to date display limited intrinsic tissue selectivity and do not discriminate between cells of different types. Here, we describe a strategy for selective protein degradation in a specific cell type. We report the design and synthesis of a trastuzumab-PROTAC conjugate (Ab-PROTAC 3) in which E3 ligase-directed degrader activity is caged with an antibody linker which can be hydrolyzed following antibody-PROTAC internalization, releasing the active PROTAC and inducing catalytic protein degradation. We show that 3 selectively targets bromodomain-containing protein 4 (BRD4) for degradation only in HER2 positive breast cancer cell lines, while sparing HER2 negative cells. Using live cell confocal microscopy, we show internalization and lysosomal trafficking of the conjugate specifically in HER2 positive cells, leading to the release of active PROTAC in quantities sufficient to induce potent BRD4 degradation. These studies demonstrate proof-of-concept for tissue-specific BRD4 degradation, overcoming limitations of PROTAC selectivity, with significant potential for application to novel targets.