Background: In the search for novel antidepressive drug candidates, bioguided fractionation of nonpolar constituents present in the oleoresin from ginger rhizomes (Zingiber officinale Roscoe, Zingiberaceae) was performed. This particular direction of the research was chosen due to the existing reports on the antidepressive properties of ginger total extract. The search for individual metabolites acting as MAO-A inhibitors, which correspond to the apparent effect of the total extract, is the subject of this work. Methods: Hexane extracts from ginger rhizomes were fractionated by using column chromatography (including silica gel impregnated with silver nitrate) and semi-preparative high-performance chromatography. For the activity assessment, an in vitro monoamine oxidase A (MAO-A) inhibition luminescence assay was performed on 10 purified terpenes: 1,8-cineole, α-citronellal, geraniol, β-sesquiphellandrene, γ-terpinen, geranyl acetate, isobornyl acetate, terpinen-4-ol, (E,E)-α-farnesene, and α-zingiberene. Results: Geraniol and (−)-terpinen-4-ol were found to be the strongest enzyme inhibitors with inhibition of 44.1% and 42.5%, respectively, at a concentration of 125 µg/mL. No differences in the inhibition potential were observed for the different groups of terpenes: sesquiterpenes, monoterpenes, or sesquiterpene alcohols; however, the two most active compounds contained a hydroxyl moiety. Conclusions: Terpene constituents from ginger’s extract were found to exhibit moderate inhibitory properties against the MAO-A enzyme in in vitro tests.