Traditional approaches for active mapping focus on building geometric maps. For most real-world applications, however, actionable information is related to semantically meaningful objects in the environment. We propose an approach to the active metric-semantic mapping problem that enables multiple heterogeneous robots to collaboratively build a map of the environment. The robots actively explore to minimize the uncertainties in both semantic (object classification) and geometric (object modeling) information. We represent the environment using informative but sparse object models, each consisting of a basic shape and a semantic class label, and characterize uncertainties empirically using a large amount of real-world data. Given a prior map, we use this model to select actions for each robot to minimize uncertainties. The performance of our algorithm is demonstrated through multi-robot experiments in diverse real-world environments. The proposed framework is applicable to a wide range of real-world problems, such as precision agriculture, infrastructure inspection, and asset mapping in factories.