Hyperspectral imagery has proven its potential in many research applications, especially in the field of environmental sciences. Currently, hyperspectral imaging is generally performed by satellite or aircraft platforms, but mini-UAV (Unmanned Aerial Vehicle) platforms (<20 kg) are now emerging. On such platforms, payload restrictions are critical, so sensors must be selected according to stringent specifications. This article presents the integration of a light pushbroom hyperspectral sensor onboard a multirotor UAV, which we have called Hyper-DRELIO (Hyperspectral DRone for Environmental and LIttoral Observations). This article depicts the system design: the UAV platform, the imaging module, the navigation module, and the interfacing between the different elements. Pushbroom sensors offer a better combination of spatial and spectral resolution than full-frame cameras. Nevertheless, data georectification has to be performed line by line, the quality of direct georeferencing being limited by mechanical stability, good timing accuracy, and the resolution and accuracy of the proprioceptive sensors. A georegistration procedure is proposed for geometrical pre-processing of hyperspectral data. The specifications of Hyper-DRELIO surveys are described through two examples of surveys above coastal or inland waters, with different flight altitudes. This system can collect hyperspectral data in VNIR (Visible and Near InfraRed) domain above small study sites (up to about 4 ha) with both high spatial resolution (<10 cm) and high spectral resolution (1.85 nm) and with georectification accuracy on the order of 1 to 2 m.