Recent reports of thrombosis following AstraZeneca COVID-19 vaccine in young females (<55 years-old) led to temporary suspension and urgent investigation by the European Medicines Agency (EMA) that concluded that vaccine benefits still outweigh its side effects (SEs). Therefore, this study aims to provide early independent evidence on the vaccine SEs’ prevalence and their potential risk factors; a cross-sectional survey-based study was carried out between February and March 2021 in Germany and Czech Republic among healthcare workers who recently received the AstraZeneca COVID-19 vaccine. The study used a validated self-administered questionnaire composed of twenty-eight multiple-choice items covering demographic variables, medical anamneses, and local, systemic, oral, and skin related SEs of the vaccine. Out of the ninety-two included participants, 77.2% were females and 79.3% were from Germany. Their mean age was 35.37 ± 12.62 (19–64) years-old, 15.2% had chronic illnesses and 22.8% were receiving medical treatments. Overall, 94.6% of the participants reported at least one SE. The most common local SE was injection site pain (72.8%), and the most common systemic SEs were fatigue (73.9%), muscle pain (55.4%), chills (48.9%), feeling unwell (46.7%), nausea (45.7%), and headache (29.3%). The vast majority (91.9%) resolved within 1–3 days, and the below 35 years-old group was the least affected age group. The SEs’ frequency was insignificantly higher in females and previously infected participants; the vaccine safety for the elderly was supported by the early findings of this study. Chronic illnesses and medical treatments were not associated with an increased risk of SE incidence and frequency. No blood disorder SEs were reported in our sample. Further independent studies are highly required to evaluate the safety of the AstraZeneca vaccine and to explore whether gender or previous infection could be associated with the vaccine SEs.