Background: The COVID-19 pandemic has raised the necessity to rapidly develop safe and effective vaccines to limit the spread of infections. Meanwhile, vaccine hesitancy is a significant barrier to community vaccination strategies. Methods: An internet-based cross-sectional survey was conducted from March to April 2021 during the start of the vaccination campaigns. Results: A total of 1009 subjects participated, and the mean age (±SD) was 29.11 ± 8.2 years. Among them, 68.8% believed that vaccination is an effective method to control the spread of the disease, 81.2% indicated acceptance of the vaccine, and 87.09% reported that their doctor’s recommendation was essential for decision making. After adjusting for socioeconomic characteristics, rural residency (AOR 1.783, 95%CI: 1.256–2.531), working a part-time job (AOR 2.535, 95%CI: 1.202–5.343) or a full-time job (AOR 1.951, 95%CI: 1.056–3.604), being a student (AOR 3.516, 95%CI: 1.805–6.852) and having a partner (AOR 1.457, 95%CI: 1.062–2.00) were significant predictors for higher vaccine acceptance among the study participants. Believing in the vaccine’s efficacy showed the strongest correlation with vaccine acceptance (Spearman’s r = 0.309, p < 0.001). Conclusions: Although general vaccine acceptance is high (32.85%) in participants in our study, gender and geographic disparities were observed in the investigated urban population of young, well-educated Egyptians.