A modular microfluidic system includes modules which are arranged next to each other in a row. Every module has a microfluidic part which rests on a contact surface of the module in a locally limited area and is forced against the contact surface by a fastening element. The microfluidic part includes a fluid channel system with fluid connections that are arranged on the top surface of the microfluidic part in edge areas relative to the adjoining microfluidic parts. The fluid connections of adjoining microfluidic parts are interlinked by respective connecting channels in a connecting part bridging the microfluidic parts, wherein the connecting part rests on the microfluidic parts in the edge areas. A clamping part rests against the lower surfaces of the adjoining microfluidic parts and is connected to the connecting part via an additional fastening element in the area between the microfluidic parts.