(1) Background: Some COVID-19 vaccine recipients show breakthrough infection. It remains unknown, which factors contribute to risks and severe outcomes. Our aim was to identify risk factors for SCoV2 breakthrough infections in fully vaccinated individuals. (2) Methods: We conducted a retrospective case-control study from 28 December 2020 to 25 October 2021. Data of all patients with breakthrough infection was compared to data of all vaccine recipients in the Canton of Basel-City, Switzerland. Further, breakthrough infections by Alpha- and Delta-variants were compared. (3) Results: Only 0.39% (488/126,586) of all vaccine recipients suffered from a breakthrough infection during the observational period, whereof most cases were asymptomatic or mild (97.2%). Breakthrough infections after full vaccination occurred in the median after 78 days (IQR 47-123.5). Factors with lower odds for breakthrough infection were age (OR 0.987) and previous COVID-19 infection prior to vaccination (OR 0.296). Factors with higher odds for breakthrough infection included vaccination with Pfizer/BioNTech instead of Moderna (OR 1.459), chronic disease (OR 2.109), and healthcare workers (OR 1.404). (4) Conclusions: Breakthrough infections are rare and mild but can occur early after vaccination. This implies that booster vaccination might be initiated earlier, especially for risk groups. Due to new variants emerging repeatedly, continuous monitoring of breakthrough infections is crucial.