Onosma roots are widely used in traditional medicine to treat various diseases throughout the world. In this study, for the first time, we investigated the component composition and biological activity of various extracts from the roots of Onosma gmelinii collected in the highlands of the Kakpakty Mountains of the Almaty region (Republic of Kazakhstan). Extracts were obtained by three different methods: percolation extraction, ultrasound-assisted extraction, and supercritical carbon dioxide extraction. The component composition of the extracts was determined by gas chromatography/mass spectrometry (GC/MS), naphthoquinones by thin-layer chromatography (TLC), and spectrophotometric method. In this study, the presence of shikonin and its derivatives in the extracts was confirmed. The concentration of naphthoquinones during CO2 extraction was about 40%, during ultrasonic extraction about 3%, and during percolation extraction about 1.3%. The GC-MS method identified 69 chemical compounds in the ultrasonic extract, 46 compounds in the CO2 extract, and 51 compounds in the percolation extract. The extracts were tested on a panel of bacteria and viruses: two Gram-negative bacteria (Escherichia coli ATCC 8739, Pseudomonas aeruginosa ATCC 9027); nine Gram-positive bacteria (Staphylococcus aureus ATCC 6538-P, Staphylococcus aureus ATCC BAA-39, Staphylococcus epidermidis ATCC 51625, Staphylococcus epidermidis ATCC 12228, Streptococcus pyogenes ATCC 19615, Streptococcus pneumoniae ATCC BAA-660, Enterococcus hirae ATCC 10541, Enterococcus faecalis ATCC 51575, Enterococcus faecium ATCC 700221); and two fungal species (Candida albicans ATCC 10231, Candida albicans ATCC 2091); five subtypes of influenza virus A (A/FPV/Weybridge/78 (H7N7), A/Swine/Iowa/15/30 (H1N1), A/black-headed gull/Atyrau/743/04 (H13N6), A/FPV/Rostock/1934 (H7N1), A/Almaty/8/98 (H3N2)). The root extracts of Onosma gmelinii showed antibacterial activity in different degrees against all tested Gram-positive bacterial strains, while no inhibitory effect on Gram-negative bacteria was observed. The results indicated that the ultrasonic extract effectively inhibits the growth of the majority of tested Gram-positive bacteria (MBC from 18.3 to 293.0 µg/mL). CO2 extract had the greatest bactericidal activity (MBC from 0.1 to 24.4 µg/mL). Percolation extract insignificantly inhibited bacterial growth (MBC from 2343.8 to 4687.5 µg/mL). CO2 extract and ultrasonic extract significantly reduced the activity of C. albicans. The results of the antiviral action showed that the ultrasonic extract has the greatest effectiveness against different subtypes of the influenza virus A, while other extracts did not show significant activity.