Optical systems for remote sensing commonly employ the principle of multi-/hyperspectral imaging, which is based on the acquisition of a set of two-dimensional images with distinct spectral bands in the ultra-violet, visible and/or infrared domain. Novel applications in the fields of environmental and agricultural monitoring, surveillance and biomedical inspection require miniaturized systems with high spectral and spatial sampling that furthermore enable a single shot image acquisition. However, conventional high resolution multi-spectral imaging solutions rely on bulky setups and depend on scanning techniques. In this work, we propose a multi-spectral imaging concept based on a multi-aperture system approach combined with a slanted linear variable spectral filter in order to overcome these restrictions. In particular, we demonstrate the optical design, fabrication and testing of a highly-compact, cost-effective multispectral imaging system, which exploits state of the art micro-optical manufacturing techniques on wafer level. The developed demonstration system incorporates a conventional full-frame format image sensor, a commercially available linear variable spectral filter and a customized microlens-array. In addition, a tailored baffle array is utilized for preventing optical crosstalk between adjacent optical channels. The setup enables the single-shot acquisition of 66 spectral channels with a linear spectral sampling over an extended wavelength range of 450-850 nm. The compact system with a size of only 60 x 60 x 28 mm3 provides a large field of view of 68° and a spatial sampling of 400x400 pixels per channel. Finally, we demonstrate its capabilities for advanced object classification by utilizing a customized multispectral analysis tool.