In the search for new bioactive agents against the infectious pathogen responsible for the neglected tropical disease (NTD) mycetoma, we tested a collection of 27 essential oils (EOs) in vitro against Madurella mycetomatis, the primary pathogen responsible for the fungal form of mycetoma, termed eumycetoma. Among this series, the EO of Santalum album (Santalaceae), i.e., East Indian sandalwood oil, stood out prominently with the most potent inhibition in vitro. We, therefore, directed our research toward 15 EOs of Santalum species of different geographical origins, along with two samples of EOs from other plant species often commercialized as "sandalwood oils". Most of these EOs displayed similar strong activity against M. mycetomatis in vitro. All tested oils were thoroughly analyzed by GC-QTOF MS and most of their constituents were identified. Separation of the sandalwood oil into the fractions of sesquiterpene hydrocarbons and alcohols showed that its activity is associated with the sesquiterpene alcohols. The major constituents, the sesquiterpene alcohols (Z)-α- and (Z)-β-santalol were isolated from the S. album oil by column chromatography on AgNO3-coated silica. They were tested as isolated compounds against the fungus, and (Z)-α-santalol was about two times more active than the β-isomer.