A phytochemical investigation of the stems of the Arabian plant Artemisia sieberi afforded three new isochlorogenic acid derivatives, namely isochlorogenic acid A-3′-O-β-glucopyranoside (1), isochlorogenic acid A-3′-O-β-glucopyranoside methyl ester (2), and isochlorogenic acid C-3′-O-β-glucopyranoside (3), obtained along with thirteen known secondary metabolites belonging to distinct structural classes. The structures of the new metabolites were elucidated by modern spectroscopic techniues based on high-resolution mass spectrometry (HR-ESIMS) and 1D/2D nuclear magnetic resonance (NMR). All isolated compounds were tested for their potential antimicrobial activity against four different bacterial strains (Bacillus subtilis, Staphylococcus aureus, Escherichia coli, and Pseudomonas aeruginosa), in addition to a fungal strain (Candida tropicalis), The results were expressed as the diameter of the clear zone (in millimetres) around each well. Compounds 1 and 3 (isochlorogenic acid A-3′-O-β-glucopyranoside and isochlorogenic acid C-3′-O-β-glucopyranoside, respectively) displayed remarkable antifungal effect and potent antibacterial activities against B. subtilis and S. aureus, respectively. 3α,4α-10β-trihydroxy-8α-acetyloxyguaian-12,6α-olide (6) and angelicoidenol 2-O-β-d-glucopyranoside (9) emerged as interesting dual antibacterial (selective on P. aeruginosa)/antifungal agents.