The nature of dark matter remains unknown to date and several candidate particles are being considered in a dynamically changing research landscape . Scalar field dark matter is a prominent option that is being explored with precision instruments such as atomic clocks and optical cavities [2-8]. Here we report on the first direct search for scalar field dark matter utilising a gravitational-wave detector operating beyond the quantum shot-noise limit. We set new upper limits for the coupling constants of scalar field dark matter as a function of its mass by excluding the presence of signals that would be produced through the direct coupling of this dark matter to the beamsplitter of the GEO600 interferometer. The new constraints improve upon bounds from previous direct searches by more than six orders of magnitude and are more stringent than limits obtained in tests of the equivalence principle by one order of magnitude. Our work demonstrates that scalar field dark matter can be probed or constrained with direct searches using gravitational-wave detectors and highlights the potential of quantum-enhanced interferometry for dark matter detection.