We use microfluidic devices to encapsulate, incubate, and manipulate individual cells in picoliter aqueous drops in a carrier fluid at rates of up to several hundred Hz. We use a modular approach with individual devices for each function, thereby significantly increasing the robustness of our system and making it highly flexible and adaptable to a variety of cell-based assays. The small volumes of the drops enables the concentrations of secreted molecules to rapidly attain detectable levels. We show that single hybridoma cells in 33 pL drops secrete detectable concentrations of antibodies in only 6 h and remain fully viable. These devices hold the promise of developing microfluidic cell cytometers and cell sorters with much greater functionality, allowing assays to be performed on individual cells in their own microenvironment prior to analysis and sorting.