MicroRNA (miRNA) sponges are vital components of posttranscriptional gene regulation. Yet, only a limited number of miRNA sponges have been identified. Here, we show that the recently evolved noncoding tumor suppressor transcript, antisense RNA to TP73 gene (TP73-AS1), functions as a natural sponge of human-specific miRNA miR-941. We find unusually nine high-affinity miR-941 binding sites clustering within 1 kb region on TP73-AS1, which forms miR-941 sponge region. This sponge region displays increased sequence constraint only in humans, and its formation can be traced to the tandem expansion of a 71-nt-long sequence containing a single miR-941 binding site in old world monkeys. We further confirm TP73-AS1 functions as an efficient miR-941 sponge based on massive transcriptome data analyses, wound-healing assay, and Argonaute protein immunoprecipitation experiments conducted in cell lines. The expression of miR-941 and its sponge correlate inversely across multiple healthy and cancerous tissues, with miR-941 being highly expressed in tumors and preferentially repressing tumor suppressors. Thus, the TP73-AS1 and miR-941 duo represents an unusual case of the extremely rapid evolution of noncoding regulators controlling cell migration, proliferation, and tumorigenesis.