Annona glabra Linn is employed in conventional medicine to treat a number of human disorders, including cancer and viruses. In the present investigation, the significant phytochemical components of Annona glabra hexane extract were identified using gas chromatography–mass spectrometry (GC-MS) analysis. Three major compounds were identified in the hexane extract: tritriacontane (30.23%), 13, 17-dimethyl-tritriacontane (22.44%), and limonene (18.97%). MTT assay was used to assess the cytotoxicity of the extract on six human cancer cell lines including liver (HepG-2), pancreas (PANC-1), lung (A-549), breast (MCF-7, HTB-22), prostate (PC-3), and colon (CACO-2, ATB-37). The extract exhibited significant cytotoxic activity against both CACO-2 and A-549 cancer cell lines (IC50 = 47 ± 0.74 μg/mL and 56.82 ± 0.92 μg/mL) in comparison with doxorubicin (IC50 = 31.91 ± 0.81 μg/mL and 23.39 ± 0.43 μg/mL) and of SI of 3.8 and 3.1, respectively. It also induced moderate-to-weak activities against the other cancerous cell lines: PC-3, PANC-1, MCF-7, and HepG-2 (IC50 = 81.86 ± 3.26, 57.34 ± 0.77, 80.31 ± 4.13, and 57.01 ± 0.85 μg/mL) in comparison to doxorubicin (IC50 = 32.9 ± 1.74, 19.07 ± 0.2, 15.48 ± 0.84 and 5.4 ± 0.22 μg/mL, respectively) and SI of 2.2, 3.1, 2.2, and 3.1, respectively. In vitro anti-HSV1 (Herpes simplex 1 virus) and HAV (Hepatitis A virus) activity was evaluated using MTT colorimetric assay with three different protocols to test protective, anti-replicative, and anti-infective antiviral activities, and three separate replications of each experiment were conducted. The plant extract showed promising protective and virucidal activity against HSV1 with no significant difference with acyclovir (79.55 ± 1.67 vs. 68.44 ± 7.62 and 70.91 ± 7.02 vs. 83.76 ± 5.67), while it showed mild protective antiviral activity against HAV (48.08 ±3.46) with no significant difference vs. acyclovir (36.89 ± 6.61). The selected main compounds were examined for their bioactivity through in silico molecular docking, which exhibited that limonene could possess the strongest antiviral properties. These findings support Annona glabra’s conventional use, which is an effective source of antiviral and anticancer substances that could be used in pharmaceuticals.