We explore the extent to which zero-shot vision-language models exhibit gender bias for different vision tasks. Vision models traditionally required task-specific labels for representing concepts, as well as finetuning; zero-shot models like CLIP instead perform tasks with an open-vocabulary, meaning they do not need a fixed set of labels, by using text embeddings to represent concepts. With these capabilities in mind, we ask: Do vision-language models exhibit gender bias when performing zero-shot image classification, object detection and semantic segmentation? We evaluate different vision-language models with multiple datasets across a set of concepts and find (i) all models evaluated show distinct performance differences based on the perceived gender of the person co-occurring with a given concept in the image and that aggregating analyses over all concepts can mask these concerns; (ii) model calibration (i.e. the relationship between accuracy and confidence) also differs distinctly by perceived gender, even when evaluating on similar representations of concepts; and (iii) these observed disparities align with existing gender biases in word embeddings from language models. These findings suggest that, while language greatly expands the capability of vision tasks, it can also contribute to social biases in zero-shot vision settings. Furthermore, biases can further propagate when foundational models like CLIP are used by other models to enable zero-shot capabilities.