Snapshot multispectral imaging (SMSI) has attracted much attention in recent years for its compact structure and superior performance. High-level image analysis based on SMSI, such as object classification and recognition, usually takes the image reconstruction as the first step, which hinders its application in many important real-time scenarios. Here we demonstrate the first, to our knowledge, reconstruction-free strategy for object detection with SMSI in the short-wave infrared (SWIR) band. The implementation of our SMSI is based on a modified 4f system which modulates the light with a random phase mask, and the distinctive point spread function in each narrowband endows the system with spectrum resolving ability. A deep learning network with a CenterNet structure is trained to detect a small object by constructing a dataset with the PSF of our SMSI system and the sky images as background. Our results indicate that a small object with a spectral feature can be detected directly with the compressed image output by our SMSI system. This work paves the way toward the use of SMSI to detect a multispectral object in practical applications.