Plant proteins of the CURVATURE THYLAKOID 1 (CURT1) family and their prokaryotic CurT homologues are key determinants of the three-dimensional structure of the thylakoid membrane systems in chloroplasts and cyanobacteria. As the evolutionary origin of the CURT1/CurT family appears to coincide with the evolution of thylakoids themselves, shaping the thylakoid system has widely been regarded as their primary role. In this study we present strong evidence that CurT, beyond regulation of thylakoid architecture, is involved in cell division and thylakoid fission/partitioning in both Synechocystis sp. PCC 6803 and Synechococcus elongatus PCC 7942, likely through physical interaction with the key cell division protein FtsZ. Similarly, triple mutants of Chlamydomonas reinhardtii CURT1A, B, and C display an asymmetric chloroplast division phenotype, thus suggesting an evolutionary conserved functionality of CurT/CURT1 in cell/chloroplast division in single-celled oxygenic photosynthesizers.