To investigate the associated factors underlying vaccination intentions for Coronavirus Disease 2019 (COVID-19), an online cross-sectional survey was conducted among adults 18 years or over in the Kingdom of Saudi Arabia. Data were collected between 8 and 14 December 2020. A logistic regression analysis was employed to examine and identify the variables associated with vaccination intentions for COVID-19, with the odds ratio (OR) and 95% confidence interval (CI) also calculated. A total of 2137 respondents completed the questionnaire. Overall, about 48% of Saudi adults were willing to receive the COVID-19 vaccine. Participants had stronger intentions to receive a vaccination if they resided in the southern region (OR: 1.95; 95% CI: 1.21–3.14), received the seasonal influenza vaccination in the past (OR: 1.52; 95% CI: 1.17–1.97), believed in mandatory COVID-19 vaccination (OR: 45.07; 95% CI: 31.91–63.65), or reported high levels of concern about contracting COVID-19 (OR: 1.91; 95% CI: 1.29–2.81). Participants were less likely to have an intention to be vaccinated if they had a history of vaccine refusal (OR: 0.28; 95% CI: 0.19–0.40). The low acceptance rate among the Saudi population should be targeted with multifaceted interventions aimed at raising awareness and emphasizing the safety and efficacy of the COVID-19 vaccine.