The ring rot of potato caused by the bacterial pathogen Clavibacter sepedonicus is a quarantine disease posing a threat to the potato industry worldwide. The sensitive and selective detection of C. sepedonicus is of a high importance for its effective control. Here, the detection system is reported to determine viable bacteria of C. sepedonicus in potato tubers, based on the coupling of CRISPR/Cas13a nuclease with NASBA (Nucleic Acid Sequence Based Amplification)—the method of isothermal amplification of RNA. Detection can be conducted using both instrumental and non-instrumental (visual inspection of test tubes under blue light) modes. When NASBA and Cas13a analyses were carried out in separate test tubes, the limit of detection (LOD) for the system was 1000 copies of purified target 16S rRNA per NASBA reaction or about 24 colony-forming units (CFUs) of C. sepedonicus per 1 g of tuber tissue. The testing can also be conducted in the “one-pot” format (a single test tube), though with lower sensitivity: LOD was 10,000 copies of target RNA or about 100 CFU per 1 g of tuber tissue for both instrumental and visual detection modes. The overall time of NASBA/Cas13a analysis did not exceed 2 h. The developed NASBA/Cas13a detection system has the potential to be employed as a routine test of C. sepedonicus, especially for on-site testing.