In this article, a novel design of compact frequency-selective rasorber exhibiting absorption–transmission–absorption characteristics and having high passband selectivity has been proposed. A square-loop resonator with mounted lossy elements serves as the elemental broadband absorber from 4 to 12 GHz. The transmission frequency at 8.4 GHz is realized by printing a Minkowski fractal-shaped resonator with a high-Q factor on the resistive layer, which provides a transmission pole at the frequency corresponding to the passband of a double-cross-slot-shaped bandpass layer. The functioning of the proposed frequency-selective rasorbers (FSR) is explained by a corresponding equivalent circuit model. The proposed FSR exhibits higher selectivity at the passband, thus making it a suitable candidate for shielding the narrowband radiating system. Measurements performed on the fabricated prototype of a 17 × 17 unit cell array provides experimental validation. Further, a low radar cross-section antenna is realized by integrating a patch antenna with the proposed FSR, which achieves an average out-of-band monostatic radar cross-section (RCS) reduction of 11.92 and 5.04 dB in the lower (4–7.5 GHz) and upper (9.2–10.8 GHz) absorption bands, respectively, while maintaining the other antenna parameters. Furthermore, the bistatic total RCS reduction of 77% and 60% are achieved in the lower and upper frequency bands, respectively.