Spectroscopic methods are established tools for nonintrusive measurements of flow velocity. However, those methods are either restricted by measuring pointwise or with low measurement rates of several hertz. To investigate fast unsteady phenomena, e.g., in sprays, volumetric (3D) measurement techniques with kHz rate are required. For this purpose, a spectroscopic technique is realized with a power amplified, frequency modulated laser and an Mfps high-speed camera. This allows fast continuous planar measurements of the velocity. Volumetric data is finally obtained by slewing the laser light sheet in depth with an oscillating microelectromechanical systems (MEMS) scanner. As a result, volumetric velocity measurements are obtained for 256×128×25 voxels over 14.4 mm×7.2 mm×6.5 mm with a repetition rate of 1 kHz, which allows the investigation of unsteady phenomena in sprays such as transients and local velocity oscillations. The respective measurement capabilities are demonstrated by experiments. Hence, a significant progress regarding the data rate was achieved in spectroscopy by using the Mfps high-speed camera, which enables new application fields such as the analysis of fast unsteady phenomena.