Nano- and micromechanical resonators are the subject of research that aims to develop ultrasensitive mass sensors for spectrometry, chemical analysis and biomedical diagnosis. Unfortunately, their merits generally diminish in liquids because of an increased dissipation. The development of faster and lighter miniaturized devices would enable improved performances, provided the dissipation was controlled and novel techniques were available to drive and readout their minute displacement. Here we report a nano-optomechanical approach to this problem using miniature semiconductor disks. These devices combine a mechanical motion at high frequencies (gigahertz and above) with an ultralow mass (picograms) and a moderate dissipation in liquids. We show that high-sensitivity optical measurements allow their Brownian vibrations to be resolved directly, even in the most-dissipative liquids. We investigate their interaction with liquids of arbitrary properties, and analyse measurements in light of new models. Nano-optomechanical disks emerge as probes of rheological information of unprecedented sensitivity and speed, which opens up applications in sensing and fundamental science.