Effective inhibition of the protein derived from cellular myelocytomatosis oncogene (c-Myc) is one of the most sought-after goals in cancer therapy. While several c-Myc inhibitors have demonstrated therapeutic potential, inhibiting c-Myc has proven challenging, since c-Myc is essential for normal tissues and tumors may present heterogeneous c-Myc levels demanding contrasting therapeutic strategies. Herein, we developed tumor-targeted nanomedicines capable of treating both tumors with high and low c-Myc levels by adjusting their ability to spatiotemporally control drug action. These nanomedicines loaded homologues of the bromodomain and extraterminal (BET) motif inhibitor JQ1 as epigenetic c-Myc inhibitors through pH-cleavable bonds engineered for fast or slow drug release at intratumoral pH. In tumors with high c-Myc expression, the fast-releasing (FR) nanomedicines suppressed tumor growth more effectively than the slow-releasing (SR) ones, whereas, in the low c-Myc tumors, the efficacy of the nanomedicines was the opposite. By studying the tumor distribution and intratumoral activation of the nanomedicines, we found that, despite SR nanomedicines achieved higher accumulation than the FR counterparts in both c-Myc high and low tumors, the antitumor activity profiles corresponded with the availability of activated drugs inside the tumors. These results indicate the potential of engineered nanomedicines for c-Myc inhibition and spur the idea of precision pH-sensitive nanomedicine based on cancer biomarker levels.