Magnetic Resonance Imaging (MRI) is a leading diagnostic modality for a wide range of exams, where multiple contrast images are often acquired for characterizing different tissues. However, acquiring high-resolution MRI typically extends scan time, which can introduce motion artifacts. Super-resolution of MRI therefore emerges as a promising approach to mitigate these challenges. Earlier studies have investigated the use of multiple contrasts for MRI super-resolution (MCSR), whereas majority of them did not fully exploit the rich contrast-invariant structural information. To fully utilize such crucial prior knowledge of multi-contrast MRI, in this work, we propose a novel structure-guided MCSR (SGSR) framework based on a new spatio-frequency co-query attention (CQA) mechanism. Specifically, CQA performs attention on features of multiple contrasts with a shared structural query, which is particularly designed to extract, fuse, and refine the common structures from different contrasts. We further propose a novel frequency-domain CQA module in addition to the spatial domain, to enable more fine-grained structural refinement. Extensive experiments on fastMRI knee data and low-field brain MRI show that SGSR outperforms state-of-the-art MCSR methods with statistical significance.