Sprouting of potatoes during storage could result in general quality losses, including weight and nutrient losses. In this work, potato tubers were treated with 18 kinds of plant essential oils during a storage period of 270 days at low temperature (3 ± 0.5 °C), and at the end of the storage period, the sprout inhibition effect, starch and reducing sugar contents were assessed. Results showed that citronella (Cymbopogon nardus) essential oil, wintergreen (Ilex chinensis Sims) essential oil, DL-menthol, jasmine (Jasminum sambac) essential oil, citral and nerol had a better sprouting control than that of CIPC (isopropyl N-(3-chlorophenyl) carbamate). Raspberry ketone was found to promote potato sprouting; the sprout length reached 5 cm at 270 days, whilst the control was 1.7 cm. On the other hand, the potatoes treated with 100 μL/L of citronella essential oil and wintergreen essential oil did not sprout, whilst the sprouting rate and sprouting index of the control were 73.33% and 23.81%, respectively. At the end of storage, the starch content of potato tubers treated with citronella essential oil and wintergreen essential oil were maintained at 15.32% and 15.80%, respectively, which was higher than that of the control (14.14%). On the contrary, the reducing sugar content of potato tubers treated with the above two essential oils were 1.28% and 1.24%, respectively, which was lower than that of the control (1.47%). These results suggest that citronella essential oil and wintergreen essential oil treatments reduced starch breakdown and reducing sugar accumulation. Therefore, citronella essential oil and wintergreen essential oil could be considered as new sprout suppressants for potato storage. Further work needs to be done at higher temperatures (8–12 °C) to confirm their effectiveness.