Bam35 and related betatectiviruses are tail-less bacteriophages that prey on members of the Bacillus cereus group. These temperate viruses replicate their linear genome by a protein-primed mechanism. In this work, we have identified and characterized the product of the viral ORF2 as a single-stranded DNA binding protein (hereafter B35SSB). B35SSB binds ssDNA with great preference over dsDNA or RNA in a sequence-independent, highly cooperative manner that results in a non-specific stimulation of DNA replication. We have also identified several aromatic and basic residues, involved in base-stacking and electrostatic interactions, respectively, that are required for effective protein-ssDNA interaction. Although SSBs are essential for DNA replication in all domains of life as well as many viruses, they are very diverse proteins. However, most SSBs share a common structural domain, named OB-fold. Protein-primed viruses could constitute an exception, as no OB-fold DNA binding protein has been reported. Based on databases searches as well as phylogenetic and structural analyses, we showed that B35SSB belongs to a novel and independent group of SSBs. This group contains proteins encoded by protein-primed viral genomes from unrelated viruses, spanning betatectiviruses and Φ29 and close podoviruses, and they share a conserved pattern of secondary structure. Sensitive searches and structural predictions indicate that B35SSB contains a conserved domain resembling a divergent OB-fold, which would constitute the first occurrence of an OB-fold-like domain in a protein-primed genome.