Telomere repeat-binding factors (TRFs) are essential components of the molecular machinery that regulates telomere function. TRFs are widely conserved across eukaryotes and bind duplex telomere repeats via a characteristic MYB-type domain. Here, we identified the telomere repeat-binding protein PfTRZ in the malaria parasite Plasmodium falciparum, a member of the Alveolate phylum for which TRFs have not been described so far. PfTRZ lacks an MYB domain and binds telomere repeats via a C2H2-type zinc finger domain instead. In vivo, PfTRZ binds with high specificity to the telomeric tract and to interstitial telomere repeats upstream of subtelomeric virulence genes. Conditional depletion experiments revealed that PfTRZ regulates telomere length homeostasis and is required for efficient cell cycle progression. Intriguingly, we found that PfTRZ also binds to and regulates the expression of 5S rDNA genes. Combined with detailed phylogenetic analyses, our findings identified PfTRZ as a remote functional homologue of the basic transcription factor TFIIIA, which acquired a new function in telomere maintenance early in the apicomplexan lineage. Our work sheds unexpected new light on the evolution of telomere repeat-binding proteins and paves the way for dissecting the presumably divergent mechanisms regulating telomere functionality in one of the most deadly human pathogens.