Acacia nilotica (synonym: Vachellia nilotica (L.) P.J.H.Hurter and Mabb.) is considered an important plant of the family Fabaceae that is used in traditional medicine in many countries all over the world. In this work, the antiviral potentialities of the chemically characterized essential oils (EOs) obtained from the bark and fruits of A. nilotica were assessed in vitro against HAV, HSV1, and HSV2. Additionally, the in silico evaluation of the main compounds in both EOs was carried out against the two proteins, 3C protease of HAV and thymidine kinase (TK) of HSV. The chemical profiling of the bark EOs revealed the identification of 32 compounds with an abundance of di- (54.60%) and sesquiterpenes (39.81%). Stachene (48.34%), caryophyllene oxide (19.11%), and spathulenol (4.74%) represented the main identified constituents of bark EO. However, 26 components from fruit EO were assigned, with the majority of mono- (63.32%) and sesquiterpenes (34.91%), where trans-caryophyllene (36.95%), Z-anethole (22.87%), and γ-terpinene (7.35%) represented the majors. The maximum non-toxic concentration (MNTC) of the bark and fruits EOs was found at 500 and 1000 µg/mL, respectively. Using the MTT assay, the bark EO exhibited moderate antiviral activity with effects of 47.26% and 35.98% and a selectivity index (SI) of 2.3 and 1.6 against HAV and HSV1, respectively. However, weak activity was observed via the fruits EO with respective SI values of 3.8, 5.7, and 1.6 against HAV, HSV1, and HSV2. The in silico results exhibited that caryophyllene oxide and spathulenol (the main bark EO constituents) showed the best affinities (ΔG = −5.62, −5.33, −6.90, and −6.76 kcal/mol) for 3C protease and TK, respectively. While caryophyllene (the major fruit EO component) revealed promising binding capabilities against both proteins (ΔG = −5.31, −6.58 kcal/mol, respectively). The molecular dynamics simulation results revealed that caryophyllene oxide has the most positive van der Waals energy interaction with 3C protease and TK with significant binding free energies. Although these findings supported the antiviral potentialities of the EOs, especially bark EO, the in vivo assessment should be tested in the intraoral examination for these EOs and/or their main constituents.