Vibrio natriegens is an emerging host for biotechnology due to its high growth and substrate consumption rates. In industrial processes typically fed‐batch processes are applied to obtain high space‐time yields. In this study, we established an aerobic glucose‐limited fed‐batch fermentation with the wild type (wt) of V. natriegens which yielded biomass concentrations of up to 28.4 gX L−1. However, we observed that the viscosity of the culture broth increased by a factor of 800 at the end of the cultivation due to the formation of 157 ± 20 mg exopolysaccharides (EPS) L−1. Analysis of the genomic repertoire revealed several genes and gene clusters associated with EPS formation. Deletion of the transcriptional regulator cpsR in V. natriegens wt did not reduce EPS formation, however, it resulted in a constantly low viscosity of the culture broth and altered the carbohydrate content of the EPS. A mutant lacking the cps cluster secreted two‐fold less EPS compared to the wt accompanied by an overall low viscosity and a changed EPS composition. When we cultivated the succinate producer V. natriegens Δlldh Δdldh Δpfl Δald Δdns::pycCg (Succ1) under anaerobic conditions on glucose, we also observed an increased viscosity at the end of the cultivation. Deletion of cpsR and the cps cluster in V. natriegens Succ1 reduced the viscosity five‐ to six‐fold which remained at the same level observed at the start of the cultivation. V. natriegens Succ1 ΔcpsR and V. natriegens Succ1 Δcps achieved final succinate concentrations of 51 and 46 g L−1 with a volumetric productivity of 8.5 and 7.7 gSuc L−1 h−1, respectively. Both strains showed a product yield of about 1.4 molSuc molGlc−1, which is 27% higher compared with that of V. natriegens Succ1 and corresponds to 81% of the theoretical maximum.