Due to significantly improved spatial and spectral resolution, hyperspectral sensors can now detect many substances that cannot be resolved by multispectral sensors. However, this comes at the price that many unknown and unidentified signal sources, referred to as interferers, may also be extracted unexpectedly. Such interferers generally produce additional noise effects on target detection and must therefore be taken into account. The problem associated with this interference is challenging because its nature is generally unknown and it cannot be identified from an image scene. This paper presents an approach, called the target-constrained interference-minimized filter (TCIMF), which does not require one to identify interferers, but can minimize the effects caused by interference. It designs a finite-impulse-response filter that specifies targets of interest in such a way that the desired targets and undesired targets will be passed through and rejected by the filter, respectively; the filter output energy resulting from unknown signal sources is also minimized. More precisely, the TCIMF accomplishes three tasks simultaneously: detection of the desired targets, elimination of the undesired targets, and minimization of interfering effects. A recently developed technique, constrained energy minimization (CEM), can be considered as a suboptimal version of the TCIMF. Computer simulations and hyperspectral image experiments are conducted to demonstrate advantages of the TCIMF over the CEM.