We propose using optomechanical interaction to narrow the bandwidth of filter cavities for achieving frequency-dependent squeezing in advanced gravitational-wave detectors, inspired by the idea of optomechanically induced transparency. This can allow us to achieve a cavity bandwidth on the order of 100 Hz using small-scale cavities. Additionally, in contrast to a passive Fabry-Pérot cavity, the resulting cavity bandwidth can be dynamically tuned, which is useful for adaptively optimizing the detector sensitivity when switching amongst different operational modes. The experimental challenge for its implementation is a stringent requirement for very low thermal noise of the mechanical oscillator, which would need a superb mechanical quality factor and a very low temperature. We consider one possible setup to relieve this requirement by using optical dilution to enhance the mechanical quality factor.