Damage to skewed bridges in recent earthquakes has reinforced the potential vulnerability of these structures. The effect of skew angle on a bridge's fragility could vary for different bridge types, ages, or geometric configurations. This paper conducts a probabilistic seismic assessment of skewed bridge performance, focusing on single-frame concrete box-girder bridge subclasses. The effect of skew angle on bridge seismic fragility is investigated for bridges with single- or two-column bents, integral or seat-type abutments, and minimal or significant levels of seismic design. Component and system-level damage states consistent with HAZUS-MH definitions are also explored in this study. The results reveal that older bridges, which are more likely to experience higher damage states, are particularly susceptible to column damage and are not sensitive to skew. Similarly, the presence of integral abutments in newer bridges significantly reduces the vulnerability and minimizes the impact of the skew angle on bridge fragility. For new bridges with seat-type abutments, the bridge skew angle has a significant effect on component and system fragility for both single- and two-column bent bridges. For these subclasses, HAZUS-MH skew factors are found to reasonably estimate the shift in median value fragility from their straight counterparts.