The quantum noise of the light field is a fundamental noise source in interferometric gravitational-wave detectors. Injected squeezed light is capable of reducing the quantum noise contribution to the detector noise floor to values that surpass the so-called standard quantum limit (SQL). In particular, squeezed light is useful for the detection of gravitational waves at high frequencies where interferometers are typically shot-noise limited, although the SQL might not be beaten in this case. We theoretically analyse the quantum noise of the signal-recycled laser interferometric gravitational-wave detector GEO 600 with additional input and output optics, namely frequency-dependent squeezing of the vacuum state of light entering the dark port and frequency-dependent homodyne detection. We focus on the frequency range between 1 kHz and 10 kHz, where, although signal recycled, the detector is still shot-noise limited. It is found that the GEO 600 detector with present design parameters will benefit from frequency-dependent squeezed light. Assuming a squeezing strength of −6 dB in quantum noise variance, the interferometer will become thermal noise limited up to 4 kHz without further reduction of bandwidth. At higher frequencies the linear noise spectral density of GEO 600 will still be dominated by shot noise and improved by a factor of 10^6dB/20dB ≈ 2 according to the squeezing strength assumed. The interferometer might reach a strain sensitivity of 6 × 10⁻²³ above 1 kHz (tunable) with a bandwidth of around 350 Hz. We propose a scheme to implement the desired frequency-dependent squeezing by introducing an additional optical component into GEO 600's signal-recycling cavity.