The goal of this research was to screen plant essential oils (EOs) as sprout inhibitors or suppressors in potato (Solanum tuberosum L.). Three controlled environment experiments were conducted to screen 18 EOs and several pure compounds as sprout inhibitors. The EOs were applied using the wicked method on potato cv. Gala in 19 L plastic containers. The results indicated that Melissa officinalis L. EO inhibited sprouting, while Coriandrum sativum L. seed oil and the EO blend of Lavandula angustifolia Mill. and Salvia sclarea L. suppressed sprouting. The EOs of interest were analyzed using gas chromatography coupled to mass spectrometry (GC-MS) and/or a flame ionization detector (GC-FID); the detailed chemical profiles are provided. The M. officinalis EO was fractionated into seven fractions, and these were tested on minitubers. We identified two fractions (F and A) that suppressed potato sprouting better than the whole oil. The GC-MS-FID analyses of M. officinalis EO fraction A identified myrcene, Z-ocimene, E-ocimene, trans-caryophyllene, and α-humulene as the main constituents, while the main constituents of fraction F were α-terpineol, β-citronellol, and geraniol. The pure isolated compounds, together with the major compound in M. officinalis EO (citral), were tested for sprout suppression on three potato cultivars (Ranger Russet, Terra Rosa, and Dakota TrailBlazer), which revealed that β-citronellol reduced the sprout length and the number of sprouts in all three cultivars, while citral and (+)-α-terpineol reduced the sprout length and the number of sprouts in Ranger Russet relative to the two controls in all three cultivars. Myrcene had a stimulating effect on the number of sprouts in Cv. Terra Rosa. However, none of the pure compounds suppressed sprouting completely or were comparable to the EO of M. officinalis.