Multimodal magnetic resonance imaging (MRI) has accelerated human neuroscience by fostering the analysis of brain structure, function, and connectivity across multiple scales and in living brains. The richness and complexity of multimodal neuroimaging, however, demands processing methods to integrate information across modalities and different spatial scales. Here, we present micapipe, an open processing pipeline for BIDS-conform multimodal MRI datasets. micapipe can generate i) structural connectomes derived from diffusion tractography, ii) functional connectomes derived from resting-state signal correlations, iii) geodesic distance matrices that quantify cortico-cortical proximity, and iv) microstructural profile covariance matrices that assess inter-regional similarity in cortical myelin proxies. These matrices are routinely generated across established 18 cortical parcellations (100-1000 parcels), in addition to subcortical and cerebellar parcellations. Results are represented on three different surface spaces (native, conte69, fsaverage5), and outputs are BIDS-conform. Processed outputs can be quality controlled at the individual and group level. micapipe was tested on several datasets and is available at https://github.com/MICA-MNI/micapipe, documented at https://micapipe.readthedocs.io/, and containerized as a BIDS App http://bids-apps.neuroimaging.io/apps/. We hope that micapipe will foster robust and integrative studies of human brain microstructure, morphology, and connectivity.